case study class 10 maths pair of linear equations

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CBSE Class 10 Maths Case Study Questions for Chapter 3 - Pair of Linear Equations in Two Variables (Published by CBSE)

Cbse's question bank on case study for class 10 maths chapter 3 is available here. these questions will be very helpful to prepare for the cbse class 10 maths exam 2022..

Case study questions are going to be new for CBSE Class 10 students. These are the competency-based questions that are completely new to class 10 students. To help students understand the format of the questions, CBSE has released a question bank on case study for class 10 Maths. Students must practice with these questions to get familiarised with the concepts and logic used in the case study and understand how to answers them correctly. You may check below the case study questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables. You can also check the right answer at the end of each question.

Check Case Study Questions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

CASE STUDY-1:

1. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?

2. How many questions did he guess?

3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?

4. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?

Let the no of questions whose answer is known to the student x and questions attempted by cheating be y

x – 1/4y =90

solving these two

x = 96 and y = 24

1. He answered 96 questions correctly.

2. He attempted 24 questions by guessing.

3. Marks = 80- ¼ 0f 40 =70

4. x – 1/4 of (120 – x) = 95

5x = 500, x = 100

CASE STUDY-2:

Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq.m.

Based on the above information, answer the following questions:

1. Form the pair of linear equations in two variables from this situation.

2. Find the length of the outer boundary of the layout.

3. Find the area of each bedroom and kitchen in the layout.

4. Find the area of living room in the layout.

5. Find the cost of laying tiles in kitchen at the rate of Rs. 50 per sq.m.

1. Area of two bedrooms= 10x sq.m

Area of kitchen = 5y sq.m

10x + 5y = 95

Also, x + 2+ y = 15

2. Length of outer boundary = 12 + 15 + 12 + 15 = 54m

3. On solving two equation part(i)

x = 6m and y = 7m

area of bedroom = 5 x 6 = 30m

area of kitchen = 5 x 7 = 35m

4. Area of living room = (15 x 7) – 30 = 105 – 30 = 75 sq.m

5. Total cost of laying tiles in the kitchen = Rs50 x 35 = Rs1750

Case study-3 :

It is common that Governments revise travel fares from time to time based on various factors such as inflation ( a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations:

Situation 1: In city A, for a journey of 10 km, the charge paid is Rs 75 and for a journey of 15 km, the charge paid is Rs 110.

Situation 2: In a city B, for a journey of 8km, the charge paid is Rs91 and for a journey of 14km, the charge paid is Rs 145.

Refer situation 1

1. If the fixed charges of auto rickshaw be Rs x and the running charges be Rs y km/hr, the pair of linear equations representing the situation is

a) x + 10y =110, x + 15y = 75

b) x + 10y = 75, x + 15y = 110

c) 10x + y = 110, 15x + y = 75

d) 10x + y = 75, 15x + y = 110

Answer: b) x + 10y = 75, x + 15y = 110

2. A person travels a distance of 50km. The amount he has to pay is

Answer: c) Rs.355

Refer situation 2

3. What will a person have to pay for travelling a distance of 30km?

Answer: b) Rs.289

4. The graph of lines representing the conditions are: (situation 2)

Answer: (iii)

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

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Class 10 Maths Case Study Questions Chapter 3 Pair of Linear Equations in Two Variables

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Case study Questions in the Class 10 Mathematics Chapter 3  are very important to solve for your exam. Class 10 Maths Chapter 3 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based   questions for Class 10 Maths Chapter 3  Pair of Linear Equations in Two Variables

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Pair of Linear Equations in Two Variables Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 3 Pair of Linear Equations in Two Variables

Case Study/Passage-Based Questions

(i) 1 st  situation can be represented algebraically as

Answer: (d) 2x+3y=46

(ii) 2 nd  situation can be represented algebraically as

Answer: (c) 3x + 5y = 74

(iii), Fare from Ben~aluru to Malleswaram is

Answer: (b) Rs 8

(iv) Fare from Bengaluru to Yeswanthpur is

Answer: (a) Rs 10

(v) The system oflinear equations represented by both situations has

Answer: (c) unique solution

Case Study 2: The scissors which are so common in our daily life use, its blades represent the graph of linear equations.

Let the blades of a scissor are represented by the system of linear equations:

x + 3y = 6 and 2x – 3y = 12

(i) The pivot point (point of intersection) of the blades represented by the linear equation x + 3y = 6 and 2x – 3y = 12 of the scissor is (a) (2, 3) (b) (6, 0) (c) (3, 2) (d) (2, 6)

Answer: (b) (6, 0)

(ii) The points at which linear equations x + 3y = 6 and 2x – 3y = 12 intersect y – axis respectively are (a) (0, 2) and (0, 6) (b) (0, 2) and (6, 0) (c) (0, 2) and (0, –4) (d) (2, 0) and (0, –4)

Answer: (c) (0, 2) and (0, –4)

(iii) The number of solution of the system of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 is (a) 0 (b) 1 (c) 2 (d) infinitely many

Answer: (d) infinitely many

(iv) If (1, 2) is the solution of linear equations ax + y = 3 and 2x + by = 12, then values of a and b are respectively (a) 1, 5 (b) 2, 3 (c) –1, 5 (d) 3, 5

Answer: (a) 1, 5

(v) If a pair of linear equations in two variables is consistent, then the lines represented by two equations are (a) intersecting (b) parallel (c) always coincident (d) intersecting or coincident

Answer: (d) intersecting or coincident

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Pair of Linear Equations in Two Variables Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Class 10 maths case study based questions chapter 3 pair of linear equations cbse board term 1 with answer key.

          Hello students, Welcome to Maths Easy Institute.  

CASE STUDY 1:   

A library is a collection of materials, books, and media that are easily accessible to everyone. Here, you can find books from different genres such that as science fiction, fiction, and many research papers. It is also a great place to socialize with your community members, which will help you build relationships with people of similar interests.

One day, two friends Sarita and Babita go to a library for some books. The library has fixed charges for the first 3 days and an additional charge for each day thereafter. If anyone takes the book for 10 days then he/she has to pay fixed charges for 3 days and additional charges for 7 days. 

Sarita take a book from Library for 7 days and paid 27 rs and Babita  take a book from Library for 5 days and paid 21 rs .

(a) If fixed charges for the library for the first 3 days is x Rs and additional charges for each day is y Rs/day then pair of linear equation satisfying the  Sarita case is:

(b)  If fixed charges for the library for first 3 days is x Rs and additional charges for each is y Rs/day then pair of linear equation satisfying Babita case is:

(c) Fixed charges and additional charges of the library is:

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Case Study Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

• Last modified on: 9 months ago
• Reading Time: 5 Minutes

Case Study Questions

Question 1:

The scissors which is so common in our daily life use, its blades represent the graph of linear equations.

Let the blades of a scissor are represented by the system of linear equations:

x + 3y = 6 and 2x – 3y = 12

(i) The pivot point (point of intersection) of the blades represented by the linear equation x + 3y = 6 and 2x – 3y = 12 of the scissor is (a) (2, 3) (b) (6, 0) (c) (3, 2) (d) (2, 6)

(ii) The points at which linear equations x + 3y = 6 and 2x – 3y = 12 intersect y – axis respectively are (a) (0, 2) and (0, 6) (b) (0, 2) and (6, 0) (c) (0, 2) and (0, –4) (d) (2, 0) and (0, –4)

(iii) The number of solution of the system of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 is (a) 0 (b) 1 (c) 2 (d) infinitely many

(iv) If (1, 2) is the solution of linear equations ax + y = 3 and 2x + by = 12, then values of a and b are respectively (a) 1, 5 (b) 2, 3 (c) –1, 5 (d) 3, 5

(v) If a pair of linear equations in two variables is consistent, then the lines represented by two equations are (a) intersecting (b) parallel (c) always coincident (d) intersecting or coincident

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Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

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CBSE 10th Standard Maths Subject Pair of Linear Equation in Two Variables Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) 2 nd situation can be represented algebraically as

(iii), Fare from Ben~aluru to Malleswaram is

(iv) Fare from Bengaluru to Yeswanthpur is

(v) The system oflinear equations represented by both situations has

(ii) Proportional expense for each person is

(iii) The fixed (or constant) expense for the party is

(iv) If there would be 15 guests at the lunch party, then what amount Mr Jindal has to pay?

(v) The system of linear equations representing both the situations will have

(ii) Represent the 2 nd situation algebraically.

(iii) If u  \(=\frac{1}{x-y} \text { and } v=\frac{1}{x+y}, \text { then } u=\)

(iv) Speed of boat in still water is

(v) Speed of stream is

(ii) Equation 3x + 6y = 18 intersects the x-axis and y-axis respectively at

(iii) Coordinates of point of intersection of two given equations are

(iv) Represent the equations, 2x + 4y = 8 and 3x + 6y = 18 graphically.

(v) System oflinear equations represented by two given lines is

(ii) Represent algebraically the situation of day- II.

(iii) The linear equation represented by day-I, intersect the x axis at

(iv) The linear equation represented by day-II, intersect the y-axis at

(v) Linear equations represented by day-I and day -II situations, are

*****************************************

Cbse 10th standard maths subject pair of linear equation in two variables case study questions with solution 2021 answer keys.

(i) (d): 1 st situation can be represented algebraically as 2x + 3y = 46 (ii) (c): 2 nd situation can be represented algebraically as 3x + 5y = 74 (iii) (b): We have, 2x + 3y = 46 .........(i) 3x+5y=74........... (ii) Multiplying (i) by 5 and (ii) by 3 and then subtracting, we get 10x - 9x = 230 - 222 \(\Rightarrow\) x = 8 \(\therefore\) Fare from Bengaluru to Malleswaram is Rs 8. (iv) (a): Putting the value of x in equation (i), we get 3y = 46 - 2 x 8 = 30 \(\Rightarrow\) Y = 10 \(\therefore\) Fare from Bengaluru to Yeswanthpur is Rs 10. (v) (c): We have, a 1  = 2, b 1 , = 3, c 1  = -46 and \(a_{2}=3, b_{2}=5, c_{2}=-74 \) \(\therefore \quad \frac{a_{1}}{a_{2}}=\frac{2}{3}, \frac{b_{1}}{b_{2}}=\frac{3}{5}, \frac{c_{1}}{c_{2}}=\frac{-46}{-74}=\frac{23}{37} \Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\) Thus system oflinear equations has unique solution.

(i) (a): 1 st situation can be represented as x + 7y = 650 ...(i) and 2 nd situation can be represented as x + 11y = 970 ...(ii) (ii) (b): Subtracting equations (i) from (ii), we get  \(4 y=320 \Rightarrow y=80\) \(\therefore\)  Proportional expense for each person is Rs 80. (iii) (c): Puttingy = 80 in equation (i), we get x + 7 x 80 = 650 \(\Rightarrow\) x = 650 - 560 = 90 \(\therefore\)  Fixed expense for the party is Rs 90 (iv) (d): If there will be 15 guests, then amount that Mr Jindal has to pay = Rs (90 + 15 x 80) = Rs 1290 (v) (a): We have a 1  = 1, b 1  = 7, c 1  = -650 and  \(a_{2}=1, b_{2}=11, c_{2}=-970 \) \(\therefore \frac{a_{1}}{a_{2}}=1, \frac{b_{1}}{b_{2}}=\frac{7}{11}, \frac{c_{1}}{c_{2}}=\frac{-650}{-970}=\frac{65}{97}\) \(\text { Here, } \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\) Thus, system of linear equations has unique solution.

Speed of boat in upstream = (x - y)km/hr and speed of boat in downstream = (x + y)km/hr. (i) (a): 1 st situation can be represented algebraically as  \(\frac{24}{x-y}+\frac{36}{x+y}=6\) (ii) (b): 2nd situation can be represented algebraically as  \(\frac{36}{x-y}+\frac{24}{x+y}=\frac{13}{2}\) (iii) (c) : Putting  \(\frac{1}{x-y}=u \text { and } \frac{1}{x+y}=v\) we get, 24u + 36v = 6 and 36u + 24v = 13/2 Solving the above equations, we get u  \(=\frac{1}{8}, v=\frac{1}{12}\) (iv) (d):  \(\because u=\frac{1}{8}=\frac{1}{x-y} \Rightarrow x-y=8\)   ........(i) \(\text { and } v=\frac{1}{12}=\frac{1}{x+y} \Rightarrow x+y=12\)   .........(ii) Adding equations (i) from (ii), we get 2x = 20 \(\Rightarrow\) x = 10 \(\therefore\) Speed of boat in still water = 10 km/hr -. (v) (c): From equation (i), 10 - y = 8 \(\Rightarrow\)  y = 2 \(\therefore\) Speed of stream = 2 km/hr.

(i) (a): At x-axis, y = 0 \(\therefore\) 2x + 4y = 8 \(\Rightarrow\) x = 4 At y-axis, x = 0 \(\therefore\) 2x + 4y = 8 \(\Rightarrow\) Y = 2 \(\therefore\) Required coordinates are (4, 0), (0, 2). (ii) (c): At x-axis, y = 0 \(\therefore\) 3x + 6y = 18 \(\Rightarrow\) 3x = 18 \(\Rightarrow\) x = 6 At y-axis, x = 0 \(\therefore\) 3x + 6y = 18 \(\Rightarrow\) 6y = 18 \(\Rightarrow\) Y = 3 \(\therefore\)  Required coordinates are (6, 0), (0, 3). (iii) (d): Since, lines are parallel. So, point of intersection of these lines does not exist. (iv) (a) (v) (a): Since the lines are parallel. \(\therefore\) These equations have no solution i.e., the given system of linear equations is inconsistent.

(i) (b): Algebraic representation of situation of day-I is 2x + y = 1600. (ii) (a): Algebraic representation of situation of day- II is 4x + 2y = 3000 \(\Rightarrow\) 2x + y = 1500. (iii) (c) : At x-axis, y = 0 \(\therefore\)   At y = 0, 2x + y = 1600 becomes 2x = 1600 \(\Rightarrow\) x = 800 \(\therefore\) Linear equation represented by day- I intersect the x-axis at (800, 0). (iv) (d) : At y-axis, x = 0 \(\therefore\) 2x + Y = 1500 \(\Rightarrow\)  y = 1500 \(\therefore\) Linear equation represented by day-II intersect the y-axis at (0, 1500). (v) (b): We have, 2x + y = 1600 and 2x + y = 1500 Since  \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} \text { i.e., } \frac{1}{1}=\frac{1}{1} \neq \frac{16}{15}\) \(\therefore\) System of equations have no solution. \(\therefore\) Lines are parallel.

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CBSE Class 10 Maths: Case Study Questions of Chapter 3 Pair of Linear Equations in Two Variables PDF Download

Case study Questions in the Class 10 Mathematics Chapter 3  are very important to solve for your exam. Class 10 Maths Chapter 3 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based   questions for Class 10 Maths Chapter 3  Pair of Linear Equations in Two Variables

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Pair of Linear Equations in Two Variables Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 3 Pair of Linear Equations in Two Variables

Case Study/Passage-Based Questions

Question 1:

(i) 1 st  situation can be represented algebraically as

Answer: (d) 2x+3y=46

(ii) 2 nd  situation can be represented algebraically as

Answer: (c) 3x + 5y = 74

(iii), Fare from Ben~aluru to Malleswaram is

Answer: (b) Rs 8

(iv) Fare from Bengaluru to Yeswanthpur is

Answer: (a) Rs 10

(v) The system oflinear equations represented by both situations has

Answer: (c) unique solution

Question 2:

The scissors which is so common in our daily life use, its blades represent the graph of linear equations.

Let the blades of a scissor are represented by the system of linear equations:

x + 3y = 6 and 2x – 3y = 12

(i) The pivot point (point of intersection) of the blades represented by the linear equation x + 3y = 6 and 2x – 3y = 12 of the scissor is (a) (2, 3) (b) (6, 0) (c) (3, 2) (d) (2, 6)

Answer: (b) (6, 0)

(ii) The points at which linear equations x + 3y = 6 and 2x – 3y = 12 intersect y – axis respectively are (a) (0, 2) and (0, 6) (b) (0, 2) and (6, 0) (c) (0, 2) and (0, –4) (d) (2, 0) and (0, –4)

Answer: (c) (0, 2) and (0, –4)

(iii) The number of solution of the system of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 is (a) 0 (b) 1 (c) 2 (d) infinitely many

Answer: (d) infinitely many

(iv) If (1, 2) is the solution of linear equations ax + y = 3 and 2x + by = 12, then values of a and b are respectively (a) 1, 5 (b) 2, 3 (c) –1, 5 (d) 3, 5

Answer: (a) 1, 5

(v) If a pair of linear equations in two variables is consistent, then the lines represented by two equations are (a) intersecting (b) parallel (c) always coincident (d) intersecting or coincident

Answer: (d) intersecting or coincident

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Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Get NCERT solutions of Chapter 3 Class 10 - Pair of Linear Equations in Two Variables at Teachoo. Answers to all exercise questions, examples and optional questions have been provided with video of each and every question

We studied  Linear Equations in Two Variables in Class 9, we will study pair of linear equations in this chapter.

In this chapter, we will learn

• What are Linear Equations in Two Variables
• Converting statements into Equations , and drawing graph of those linear equations
• Possible Type of Graphs for Pair of Linear Equations in Two Variables - Two Lines Intersecting, Two lines Parallel, Coincident Lines
• Finding s olution of equations from graphs
• Consistency of equations  by finding ratio of a 1 /a 2 , b 1 /b 2 , c 1 /c 2
• Intersecting Lines (Exactly one solution - unique)
• Coincident Lines (Infinitely many solutions)
• Parallel Lines ( No solutions)
• Substitution Method
• Elimination Method
• Cross Multiplication Method
• Solving complicated equations like 2/x + 3/y = 4 by substituting variables (like putting p = 1/x, q = 1/y and solving)
• Solving Statement Questions by first forming equations, and then solving

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• Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables 2024-25

CBSE Class 10 Maths Important Questions Chapter 3 - Pair of Linear Equations in Two Variables - Free PDF Download

The beginning of a student's career starts with their first board exam of class 10. Class 10 results determine a student's career and their focus on the subject they want to study and proceed with. We say mathematics is the key to all topics, and it only gets harder with growing class. It is the only subject that requires a lot of practice and concentration. 

Like other subjects, you cannot learn mathematics. A lot of practice, concentration, and knowledge are the only ways to get the perfect score. Therefore, everyday practice and concentration will help one to get through the exam easily. 

Here we discuss the third chapter of class 10 maths , Linear equations. It is one of the introductory mathematics branches that will help the students excel in competitive exams. The Pair of Linear Equations in two variables is an important chapter and consists of various maths problems. We have assembled some important questions for class 10 maths chapter 3 , which will help the students have a thorough revision before the exams. 

Download CBSE Solutions for all subjects for free from Vedantu. Students can register and download Class 10 Maths and Class 10 Science NCERT Solutions and solutions of other subjects for free.

Download CBSE Class 10 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 10 Maths Important Questions for other chapters:

Related Chapters

Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

Class 10 is a crucial year for every student's career and an important step towards their future. No matter which subject the student wants to study, it is impossible to accomplish the year without proper concentration and knowledge. 

Every year, thousands of students choose mathematics for their career and fail to score good grades due to lack of practice. Mathematics requires daily exercise and a routine that every student should follow. 

Without proper practice, it is not possible to understand where to place which formula and solve the problems. Here, we have assembled extra questions for class 10 maths chapter 3 . 

These PDF questions are prepared by Vedantu experts and are free for the students to download and practice. The teachers have prepared the question-answer set for the students according to new CBSE guidelines . The students can easily cover the entire chapter and all sorts of questions coming for their final exams. These questions cover most of the topics and are extremely reliable. It will boost your confidence and help you solve all types of questions that the examiners can set. 

Chapter 3 Maths Class 10 Important Questions

Mathematics is not an easy subject that anyone can solve just by studying before a few days of examination. Especially, class 10 is crucial with high-level mathematics problems for the students to solve. Therefore, daily practices will help students memorize the formulas and understand the types of issues that might come up during their finals. Expert mathematicians of Vedantu have prepared a set of important questions of chapter 3 Maths class 10 , which will help the students revise the chapter easily. The pdf is free for the students who register for the site. 

What are Linear Equations?

Equations with first order are known as linear equations. The word linear defines the equation is in a line of the coordinate system. Therefore, any equation lying in a straight line is known as a linear equation. y=mx+b resembles the definition of a straight line where b is the intercept and m is the slope of the line. These equations consist of the highest exponent of variables as one and hence, are known as first-degree equations.

There are various types of linear equations. When an equation has only one variable or a homogeneous variable, then that type is known as a linear equation with one variable. In other words, an equation in a line is achieved by relating zero to any field of linear polynomial from which we can obtain the coefficients id known as a linear equation with one variable. 

The answers of linear equations produce values that make a true equation when exchanged with unknown values. There is only one solution available for one variable, like x+2=0. However, when it comes to two variables linear equation, the Euclidean plane's answer is calculated as Cartesian coordinates. 

Forms of Linear Equation

A line is determined in an X-Y plane through various forms. Here, we have a list of some common conditions which we use to solve linear equations. 

Slope Intercept Form

General Form

Intercept Form

Two-point Form

The Standard Form of Linear Equations

The combination of variables and constants form a linear equation. A linear equation with one variable is depicted as ax+b=0, where x is a variable, and a≠0. 

The standard form of linear equation with two variables is depicted as ax+by+c=0, where a is not equal to zero, b is not equal to zero, and x and y are variables. 

The standard form of a linear equation with three variables is depicted as ax+by+cz+d=0, where a, b and c are not equal to zero and x, y, z are variables. 

The most common way to solve linear equations is in the slope-intercept form. It is represented as y=mx+c, where y and x are the x-y plane points, c is the intercept with a constant value and m is the slope of the line known as a gradient. 

For example, y=5x+9

Slope, m=5, and intercept=9.

Point Slope Form

Considering the points on the x-y plane, a straight line equation is formed as the linear equation. It is represented as y-1=m(x-x 1 ), where the coordinates of the line are x 1 and y 1 . The other way of representing it is y=mx+y 1 -mx 1 .

The intercept form is represented when the axes of the lines intersect in two different points on the x-y plane and are neither parallel to the y-axis or the x-axis. In the equation, x/x 0 +y/y 0 =1, the values of x 0 and y 0 are not equal to zero. 

Two Point Form

Suppose (x 1 ,y 1 ) and (x 2 ,y 2 ) are two points, and only one line passes through these points, then the linear equation is represented as 

y-y 1 =[(y 2 -y 1 )/(x 2 -x 1 )](x-x 1 ) where x 1 ≠x 2 and (y 2 -y 1 )/(x 2 -x 1 ) is the slope of the line.

Solving Linear Equations with One Variable

To solve a linear equation, you must balance both sides of the equation. When you place the equality sign in between the equation, it denotes that the value on both sides of the equation is equal. The balanced equation requires specific ways of solving it as you cannot change anyone side's value. To find the value of x, the first step is to simplify both sides and then put all the x consonants on one side, finding out the value of x. 

Solving Linear Equations with Two Variables

There are different methods that you can use to solve linear equations with two variables. 

Substitution method

Cross multiplication method

Elimination method

Determinant methods

When looking for values of the variables like x and y, it is important to solve two sets of equations. Since a single equation can have an infinite amount of solutions. Suppose, ax+by+c=0 and dx+ey+f=0, where x and y are variables and a≠0, b≠0, c≠0, d≠0, and e≠0.

Class 10 Maths Chapter 3 Extra Questions For Students to Practice

In the equation y=0, and y= -5, find the number of solutions. 

Find the value of (x+y) from the two equations, ax+by=a²-b², and bx+ay=0. 

Find if the following linear equations are inconsistent or consistent, 3x+2y=8, 6x-4y=9.

Draw the graph of 2x=y+3, 2y=4x-6, and check if the equation has a unique solution. 

Draw the equations on graph paper where the coordinates of the points intersect the lines at the y-axis. x+3y=6, 2x-3y=12. 

Solve x and y: 10/x+y +2/x-y =4; 15/x+y - 5/x-y =-2

Solve the pair of linear equations. 141x +93y =189; 93x+141y=45

Solve by elimination method: 3x= y+5, 5x-y=11.

Find the values of x and y: 27x+31y=85; 31x+27y=89

Find two numbers that have a sun of 75 and a difference of 15.

Benefits of CBSE Class 10 Maths Chapter 3 Important Questions

Class 10 students often face trouble with mathematics, and they often find it difficult to score good marks. With so many chapters and the number of formulas, it is impossible to remember everything. This is the reason; the set of questions help the students to revise the chapters. 

The important question of ch 3 maths class 10 will help the students to practice last minute mathematics and revise the chapter covering all types of problems. 

The set of important questions involve every kind of questions that might come in the exams. 

Extra questions for class 10 maths chapter 3 is available for all the students on the Vedantu website.

Class 10 is a crucial year for every student, and covering all mathematics topics is important to score good grades. This set of important questions will help the students to cover all the issues and score good marks. 

Important Related Links for CBSE Class 10 Maths

FAQs on Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables 2024-25

1. Where can we avail the Important questions for class 10 maths chapter 3 linear equations in two variables?

The most accurate and reliable  Important questions for class 10 maths chapter 3 linear equations in two variables are available on Vedantu as a free PDF download to help students. Prepared by subject matter experts these are one of the most reliable and irreplaceable study material for the students. With the Important questions, Vedantu provides students with mock papers, sample papers, solved previous years question papers along with NCERT Solutions along with answers to make studying as flawless as possible for the students. Along with these study materials, students can avail LIVE online classes on Vedantu to make they’re studying a more realistic and productive activity to obtain maximum results.

2.  What do the Important Questions for Class 10 Maths hold?

The important questions for Class 10 Maths hold all the questions that are important from the exam point of view. This is a very important material as they cover the topics which the students would tend to forget to study them or would have missed them during their study session. These questions cover most of the important topics and chapters in the form of solved questions that help students learn better. These important questions will help you to revise each and every important topic in the syllabus. Also, these important questions are a great way of revising and testing yourself once you finish studying the entire syllabus.

3. What is the general form of a Linear Equation in Two Variables? What is the Solution of a Linear Equation in 2 variables?

The general form of a linear equation in two variables is -  ax + by + c = 0, where a and b cannot be zero simultaneously.

The solution of a linear equation in two variables is a pair of values, one for x and the other for y. These two values must make the two sides of the equation equal.

Eg: If 4x + y = 14, then (2,6) is one of its solutions as it satisfies the equation.

Note: A linear equation in two variables has infinite solutions.

4. What are the different ways of finding solutions to a linear equation in two variables?

The different ways of finding solutions to a linear equation in two variables are mentioned below:

Cross-multiplication method

Graphical method

5. What tips should be followed by a student to prepare Chapter 3 of Class 10 Maths?

For preparing Chapter 3 of Class 10 Maths, the following tips should be followed by the students:

Refer to the Maths NCERT book for understanding the concepts of Chapter 3 of Class 10 Maths.

Solve every exercise and example to comprehend the chapter in a better way.

Try to attend the school lectures as you will be able to understand the chapter more easily.

Go through the previous years question papers to know about the pattern of the exam.

6. What are the various topics included in Chapter 3 of Class 10 Maths?

The several concepts covered in Chapter 3 of Class 10 Maths are:

Introduction

Pair of Linear Equations in Two Variables

Discovering Solution Graphically for a Pair of Linear Equations

Solving a Pair of Linear Equations with the help of Algebraic Methods

            I. Substitution Method

            II. Elimination Method

            III. Cross-Multiplication Method

Reduction of a Set of Linear Equations in Two Variables

Students have to be thorough with these topics to solve questions related to the chapter.

7. What is the method of finding the existence of solutions for a pair of linear equations?

The Linear equations are represented by two lines in the graphical method. 

To find their solutions consider the following points:

If the pair of equations is consistent then the lines will cut each other at a common point. This means that these equations will have a unique solution.

There are infinitely many solutions for that pair of equations for which the two lines will coincide with each other. These equations are dependent.

The pair of equations will have no solution if the lines are parallel. In this case, these equations are inconsistent.

8. What is the basic concept behind the topic "Pair of Linear Equations in Two Variables"?

This topic is taken from Chapter 3 of Class 10 Maths. In this topic, students will learn about the general format for writing linear equations in two variables. The equation is presented in the form of "ax + by + c = 0" where a and b are non-zero and real numbers. The solution for the equations is defined as those values of x and y, which makes the two equations equal. As the equation is represented by a line, therefore, the solution of the equation is a point on that line.

9. Is it possible to download important questions of Chapter 3 of Class 10 Maths?

Yes, it is. Students can download the important questions of Chapter 3 of Class 10 Maths by following the given steps:

Visit the page-Important questions for Chapter 3 of Class 10 Maths .

Vedantu' s official website will open.

After the opening of the website, you will see that the important questions of Chapter 3 of Class 10 Maths are available there.

On top of the provided important questions, you will discover the option of "Download PDF".

Click that option and the PDF file will be downloaded free of cost.

Students can also visit the Vedantu app to download the study material free of cost.

CBSE Class 10 Maths Important Questions

Cbse study materials.

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

Revised NCERT Solutions for Class 10 Maths chapter 3 Pair of linear equations in two variables all exercises answer in Hindi and English medium updated for 2024-25. As per the new textbooks issued for academic year 2024-25, there are only three exercises in chapter 3 of class 10th mathematics.

Class 10 Maths Chapter 3 Solutions for Board Exams

• Class 10 Maths Chapter 3 Exercise 3.1
• Class 10 Maths Chapter 3 Exercise 3.2
• Class 10 Maths Chapter 3 Exercise 3.3

Class 10 Maths Chapter 3 Solutions for State Boards

• Class 10 Maths Chapter 3 Exercise 3.4
• Class 10 Maths Chapter 3 Exercise 3.5
• Class 10 Maths Chapter 3 Exercise 3.6
• Class 10 Maths Chapter 3 Exercise 3.7

Class 10th Maths Chapter 3 Solutions

• Class 10 Maths Chapter 3 NCERT Book
• Class 10 Maths NCERT Solutions
• Class 10 all Subjects NCERT Solutions

According to new syllabus the class 10th math has only three exercise for board exams. Exercise 3.1 is deleted now. The exercise 3.2 become ex. 3.1, Exercise 3.3 become ex. 3.2 and exercise 3.4 become ex. 3.3 now. The split up syllabus for 10th mathematics chapter 3 is as follows: Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.

• Now, Number of exercise: 3
• Number of Period needed: 15
• Weightage of the Chapter: 7 -8

UP Board students (High School and Intermediate) are now using NCERT Textbooks for most of the subjects. Class 10 Mathematics Books for UP Board is same as the NCERT Books for Class 10 Math in CBSE Board. So, the students of Uttar Pradesh Board can download, UP Board Solutions for class 10 Math Chapter 3 from this page of Tiwari Academy. Solutions are available in Hindi and English Medium. Graphs are given for all the questions if required. Visit to Discussion Forum to ask your questions. You can reply the questions already asked by other users.

Class 10 Maths Chapter 3 Practice Tests with Answers

• Class 10 Maths Chapter 3 Practice Test 1
• Class 10 Maths Chapter 3 Practice Test 2
• Class 10 Maths Chapter 3 Practice Test 3
• Class 10 Maths Chapter 3 Practice Test 4
• Class 10 Maths Chapter 3 Practice Test 5
• Class 10 Maths Chapter 3 Practice Test 6

In NCERT Solutions Class 10, all exercises are solved in both English as well as in Hindi medium in order to help all type of students for academic session 2024-25. In Maths 10, Exercise 3.1, 3.2, and 3.3 solutions, if there is any inconvenient to understand, please inform us, we will try to solve it. All NCERT Solutions 2024-25 are made for the CBSE exam for March, 2022 based on latest CBSE Syllabus 2024-25.

Changes in CBSE Syllabus for Class 10 Maths Chapter 3

CBSE has reduced the syllabus of all subjects in all the classes. The CBSE Syllabus for Class 10 Maths is reduced to 65 percent now. The changes in 10th Maths chapter 3: Linear equations in two variables are given below.

The new CBSE Syllabus for 2024-25 Class 10 Maths Chapter 3

Pair of linear equations in two variables and graphical method of their solution, consistency /inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems. Simple problems on equations reducible to linear equations.

Deleted Section from previous Syllabus

Solution of a pair of linear equations in two variables by Cross-multiplication.

Previous Years Questions – 1 Mark or 2 Marks

1. Find whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident: 3x + y = 7 & 6x + 2y = 8. [CBSE 2016] 2. Find the value of k for which the system of equations 3𝑥 − 4𝑦 = 7; 𝑘𝑥 + 3𝑦 − 5 = 0 has no solution. [CBSE 2014] 3. A father is three times as old as his son. After five years, his age will be two and a half times as old as his son. Represent this situation algebraically only. [CBSE 2013] 4. For which value of p does the pair of equations given below have a unique solutions? 4x + py + 8 = 0; 2x + 2y + 2 = 0. [CBSE 2010, 2011, 2013] 5. For what value of k, the following system of linear equations has no solutions? 3x + y = 1; (2k – 1)x + (k – 1)y =2k + 1. [CBSE 2010, 2011, 2012]

Previous Years Questions – 3 Marks

1. Solve for x and y: 11/x – 1/y = 10 & 9/x – 4/y = 5. [CBSE 2016] 2. Solve using cross multiplication method: 5x + 4y – 4 = 0 & x – 12y – 20 = 0. [CBSE 2016] 3. A man has certain notes of denomination ₹ 20 and ₹ 5 which amount to ₹380. If the number of notes of each kind are interchanged, they amount to ₹60 less than before. Find the number of notes of each denomination. [CBSE 2015] 4. Find the value of ‘k’ for which the following system of equations represents a pair of coincident lines: 𝑥 + 2𝑦 = 3; (𝑘 − 1)𝑥 + (𝑘 + 1)𝑦 = 𝑘 + 3. [CBSE 2014] 5. Check graphically, whether the pair of equations x + 3y = 6 & 2x – 3y = 12 is consistent. If so, then solve them graphically. [CBSE 2013] 6. The path of a train A is given by the equation x + 2y – 4 = 0 and path of another train B is given by the equation 2x + 4y – 12 = 0. Represent this situation graphically and find whether the two trains meet each other at some place. [CBSE 2013] 7. Form a pair of linear equations in two variables from the data given and solve it graphically: Tina went to a book shop to get some story books and textbooks. When her friends asked her how many of each she had bought, she answered – ‘The number of textbooks is two more than twice the number of story books bought. Also, the number of textbooks is four less than four times the number of story books bought. Help her friends to find the number of textbooks and story books she had bought. [CBSE 2013] 8. Determine graphically, the coordinates of the vertices of a triangle whose sides are graphs of the equations 2x – 3y + 6 = 0, 2x + 3y – 18 = 0 and y – 2 = 0. Also, find the area of this triangle . [CBSE 2010, 2011]

Previous Years Questions – 4 Marks

1. For Uttarakhand flood victims’ two sections A and B of class X contributed ₹ 1500. If the contribution of X A was ₹ 100 less than that of X B, find graphically the amounts contributed by both the sections. [CBSE 2016] 2. Three lines 3x + 5y = 15, 6x – 5y = 30 and x = 0 are enclosing a beautiful triangular park. Find the points of intersection of the lines graphically and the area of the park if all measurements are in km. [CBSE 2016] 3. Some people collected money to be donated in two Old Age Homes. A part of the donation is fixed and remaining depends on the number of old people in the home. If they donated ₹ 14500 in the home having 60 people and ₹ 19500 with 85 people, find the fixed part of donation and the amount donated for each people. What is the inspiration behind this? [CBSE 2016] 4. While teaching about the Indian National flag, teacher asked the students that how many lines are there in Blue colour wheel? One student replies that it is 8 times the number of colours in the flag. While other says that the sum of the number colours in the flag and number of lines in the wheel of the flag is 27. Convert the statements given by the students into linear equation of two variables. Find the number of lines in the wheel. [CBSE 2015] 5. Determine the value of k for which the following system of linear equations has infinite number of solutions: (k – 3)x + 3y = k & kx + ky = 12. [CBSE 2015] 6. Draw the graph of the following pair of linear equation: x + 3y = 6 & 2x – 3y = 12. Find the ratio of the areas of the two triangles formed by first line, x = 0, y = 0 and second line, x = 0, y = 0. [CBSE 2015] 7. Places A and B are 200km apart on a high way. One car starts from A and another from B at the same time. If the cars travel in the same directions at different speeds, they meet in 10 hours. Find the speeds of the two cars. [CBSE 2014] 8. Show graphically that the system of equations𝑥 + 2𝑦 = 4 and 7𝑥 + 4𝑦 = 18 is consistent with a unique solution (2, 1). [CBSE 2014]

10th Maths Chapter 3 Questions for Practice

1. Solve for x and y: 99x + 101y = 1499; 101x + 99y = 1501. [CBSE 2010, 2011, 2012, 2013, 2014] 2. The age of father is equal to sum of ages of his 4 children. After 30 years, sum of the ages of the children will be twice the age of the father. Find the age of the father. [CBSE 2013] 3. A person can row a boat 8 km upstream and 24 km downstream in 4 hours. He can row 12 km downstream and 12 km upstream in 4 hours. Find the speed of rowing in still water and the speed of the current. [CBSE 2013] 4. Solve for x and y: 37x + 43y = 123; 43x + 37y = 117. [CBSE 2010, 2011, 2012] 5. Draw the graph of the equations: x – y + 1 = 0 & 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x – axis and shade the triangular region. Also calculate the area of the triangle so formed. [CBSE 2011] 6. The sum of a 2 digit number and number obtained by reversing the order of digits is 99. If the digits of the number differ by 3, find the number. [CBSE 2011] 7. Check graphically whether the pair of linear equations 4x – y – 8 = 0 and 2x – 3y + 6 = 0 is consistent. Also determine the vertices of the triangle form by these lines and x – axis. [CBSE 2006, 2011] 8. The sum of the digits of a two digit number is 9. Nine times this number is twice the number obtained by reversing the digits. Find the number. [CBSE 2010] 9. A leading library has a fixed charge for the first three days and an additional charge for each day thereafter. Sarita paid ₹ 27 for a book kept for seven days. While Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day. [CBSE 2010] 10. Solve the following system of linear equations by elimination method: 6(ax + by) = 2a + 2b and 6(bx – ay) = 3b – 2a. [CBSE 2006, 2004]

Historical Facts !

History about Linear Equations with two variables. Around 4000 years ago, Babylon knew how to solve a simple linear equation with two variables. Around 200 BC, the Chinese published that “Nine Chapters of the Mathematical Art,” they displayed the ability to solve a system of equations in three variables (Perotti). Evidence from about 300 BC indicates that the Egyptians also knew how to solve problems involving a system of two equations in two unknown quantities, including quadratic equations. Euler brought to light the idea that a system of equations doesn’t necessarily have to have a solution (Perotti). He recognized the need for conditions to be placed upon unknown variables in order to find a solution. With the turn into the 19th century Gauss introduced a procedure to be used for solving a system of linear equations. Cayley, Euler, Sylvester, and others changed linear systems into the use of matrices to represent them. Gauss brought his theory to solve systems of equations proving to be the most effective basis for solving unknowns.

How many exercises are there in Class 10 Maths chapter 3?

There are in all 7 exercises in class 10 mathematics chapter 3 (Pair of linear equations in two variables).

• In second exercise (Ex 3.1), there are in all 7 questions.
• In third exercise (Ex 3.2), there are in all 3 questions.
• In fourth exercise (Ex 3.3), there are only 2 questions.
• So, there are total 12 questions in class 10 mathematics chapter 3 (Pair of linear equations in two variables).
• In chapter 3 of 10th Maths there are in all good examples. Examples 4, 5, 6 are based on Ex 3.1, Examples 7, 8, 9, 10 are based on Ex 3.2, Examples 11, 12, 13 are based on Ex 3.3.

What are the most important questions of 10th Maths Chapter 3?

• In second exercise (Ex 3.1), all questions are important.
• In third exercise (Ex 3.2), Q1 (iv, v, vi), 2, 3 are important.
• In fourth exercise (Ex 3.3), Q2 is important.
• Important examples of chapter 3 (Pair of linear equations in two variables) class 10th mathematics are examples 1, 2, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19.

Which chapter should recall before starting class 10th Math chapter 3?

Yes, before starting class 10th mathematics chapter 3 (Pair of linear equations in two variables), students should recall chapter 4 (Linear Equations in Two Variables) of class 9th mathematics.

What are real life applications of class 10th Maths chapter 3?

Some real life applications of class 10th mathematics chapter 3 (Pair of linear equations in two variables) are: To solve age related problems. Example: Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages? To solve speed, distance and time related problems. Example: Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? To solve cost related problems. Examples: The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs1750. Find the cost of each bat and each ball. To solve geometry problems. Example: In a ∆ABC, ∠ C = 3 ∠ B = 2 (∠A + ∠ B). Find the three angles.

« Chapter 2: Polynomials

Chapter 4: quadratic equations ».

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NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

NCERT solutions for class 10 maths chapter 3 Pair of Linear Equations in Two Variables enables the students to understand and explore simple ways to solve linear equations. This is a chapter that is widely used in industrial applications. It is used to solve questions based on speed-distance, money percentage, age, force-pressure, and so on. The kids will cover algebraic methods of solving a pair of linear equations in two variables, like the elimination method, the cross-multiplication method, and equations reducible to a pair of linear equations in two variables.

The NCERT solutions class 10 maths chapter 3 Pair of Linear Equations in Two Variables teaches that the general form of a linear equation in two variables is ax + by + c = 0, where x and y are variables and a, b and c are real numbers. Now, in this equation, the constants with variables cannot be equal to zero simultaneously. Such equations have two values, each for ‘x’ and ‘y’, which make both sides of the equation equal. The class 10 maths NCERT solutions chapter 3 Pair of linear equations in two variables can be accessed through the links below and also you can find some of these in the exercises given below.

• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.1
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.2
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.3
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.4
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.5
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.6
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.7

NCERT Solutions for Class 10 Maths Chapter 3 PDF

Linear equations are implemented to overcome real-world problems in a variety of fields. To evaluate this type of equation, we must either apply the substitution technique or mathematical elimination, which is explained with appropriate examples in the NCERT solutions class 10 maths chapter 3 Pair of linear equations in two variables. The pdf of the different exercises in the chapter can be found below :

☛ Download Class 10 Maths NCERT Solutions Chapter 3

NCERT Class 10 Maths Chapter 3   Download PDF

A linear equation in two variables can also be easily represented on a graph. Since the equation forms a straight line , and a line can have infinitely many solutions so each solution can be uniquely plotted on the graph . Equations aren't simply a theoretical concept; they're also incredibly useful in everyday situations; hence, it is essential that the students get a practical problem-solving approach with the help of the examples and questions presented in the chapter. A section-wise quick analysis of the exercise questions in the NCERT Solutions Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables can be seen below :

• Class 10 Maths Chapter 3 Ex 3.1 - 3 Questions
• Class 10 Maths Chapter 3 Ex 3.2 - 7 Questions
• Class 10 Maths Chapter 3 Ex 3.3 - 3 Questions
• Class 10 Maths Chapter 3 Ex 3.4 - 2 Questions
• Class 10 Maths Chapter 3 Ex 3.5 - 4 Questions
• Class 10 Maths Chapter 3 Ex 3.6 - 2 Questions
• Class 10 Maths Chapter 3 Ex 3.7 - 8 Questions

Topics Covered: The topics covered in class 10 maths NCERT Solutions chapter 3 include the definition of linear equations, graphical method of a solution of a pair of linear equations, algebraic methods of solving a pair of linear equations by elimination, substitution, and cross multiplication , as well as equations reducible to a pair of linear equations.

Total Questions: Class 10 maths chapter 3 Pair Of Linear Equations In Two Variables consists of 29 questions, of which 12 are long answers, 8 are moderate-level, and 9 are easy problems. These sums are solved in a step-wise manner so that students can get a conceptual understanding of the topics covered in this chapter.

List of Formulas in NCERT Solutions Class 10 Maths Chapter 3

Formulas give a way to simplify a tough sum and solve it more efficiently. A pair of linear equations can be solved using two methods, one is the algebraic method, and the other is the graphical method. In order to use these techniques, we need to cover topics such as the standard form of linear equations, equations for simultaneous pairs, etc. It is advised that kids make a formula chart that outlines the steps needed to be used when attempting such problems. This also helps them to revise the chapter at a steady pace and efficiently. Some of the important equations from this chapter of NCERT Solutions have been mentioned below:

• Pair of linear equations in two variables :

x = a 1 x + b 1 y + c 1 = 0 : y = a 2 x + b 2 y + c 2 = 0

The above two equations signify the general form of a system of linear equations that can be solved using elimination and substitution methods.

• Cross Multiplication Method : If a pair of linear equations given by a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0, then the following conditions are possible :
• a 1 /a 2 ≠ b 1 /b 1 : depicting consistent pair of linear equations
• a 1 /a 2 = b 1/ b 2 ≠ c 1/ c 2 : depicting inconsistent pair of linear equations
• a 1 /a 2 = b 1 /b 2 = c 1 /c 2 : depicting dependent as well as consistent pair of linear equations

Important Questions for Class 10 Maths NCERT Solutions Chapter 3

Video solutions for class 10 maths ncert chapter 3, faqs on ncert solutions class 10 maths chapter 3, why are ncert solutions class 10 maths chapter 3 vital for scoring well.

NCERT solutions class 10 maths chapter 3 have been prepared by experts and provide practical and graphical methods of solving a pair of linear equations with examples. The important topics such as consistent, inconsistent, and dependent pair of equations in two variables are explained in a step-wise manner with appropriate examples. Also, the CBSE board recommends studying NCERT solutions making them a vital resource.

Do I Need to Practice all Questions Given in Class 10 Maths NCERT Solutions Linear Equations in Two Variables?

The NCERT solutions class 10 maths linear equations in two variables have examples and exercise questions that cover the important topics in detail and will help to build a strong foundation for students. The set of questions cover both algebraic and graphical problems. The more kids will practice all the problems, the better clarity they will get on the concepts. Hence, it's essential that the students aim to solve all the questions.

What are the Important Topics Covered in NCERT Solutions Class 10 Maths Chapter 3?

The important topics covered in the NCERT solutions class 10 maths chapter 3 are the definition of a linear equation, degrees of an equation, as well as the elimination and substitution method. NCERT solutions help the students learn how to multiply the equations. They will also come across new terms like consistent, inconsistent pair of linear equations, point of intersection, and many more.

How Many Questions are there in Class 10 Maths NCERT Solutions Chapter 3?

The NCERT Solutions contain a total of 29 well-researched questions that include both graph-based as well as algebraic sums. These 29 questions are distributed across 7 exercises. Students must go through all the examples before solving these exercises. Each question has been solved in a detailed manner with appropriate explanations in the NCERT solutions class 10 maths chapter 3.

What are the Important Formulas in NCERT Solutions Class 10 Maths Chapter 3?

The important formulas mentioned in the NCERT Solutions class 10 maths chapter 3 are formulas for the cross-multiplication and division methods. Students must also remember the standard form of linear equations in two variables, as well as their general equations. These formulas are very important from an exam perspective and can help students solve questions in minutes. In order to understand the derivation of these formulas, kids must go through the theory of the chapter.

Why Should I Practice NCERT Solutions Class 10 Maths Chapter 3?

NCERT solutions focus on equations reducible to a pair of linear equations in two variables. Practicing the elimination and substitution methods will help students master NCERT solutions class 10 maths chapter 3. Questions related to these topics are frequently asked in board exams hence it is important to go through these solutions on a regular basis in order to score excellent marks.

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CBSE Class 10 Maths Case Study

CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam. Selfstudys has provided below the chapter-wise questions for CBSE Class 10 Maths. Students must solve these case study based problems as soon as they are done with their syllabus. 

These case studies are in the form of Multiple Choice Questions where students need to answer them as asked in the exam. The MCQs are not that difficult but having a deep and thorough understanding of NCERT Maths textbooks are required to answer these. Furthermore, we have provided the PDF File of CBSE Class 10 maths case study 2021-2022.

Class 10 Maths (Formula, Case Based, MCQ, Assertion Reason Question with Solutions)

In order to score good marks in the term 1 exam students must be aware of the Important formulas, Case Based Questions, MCQ and Assertion Reasons with solutions. Solving these types of questions is important because the board will ask them in the Term 1 exam as per the changed exam pattern of CBSE Class 10th.

Important formulas should be necessarily learned by the students because the case studies are solved with the help of important formulas. Apart from that there are assertion reason based questions that are important too. 

Assertion Reasoning is a kind of question in which one statement (Assertion) is given and its reason is given (Explanation of statement). Students need to decide whether both the statement and reason are correct or not. If both are correct then they have to decide whether the given reason supports the statement or not. In such ways, assertion reasoning questions are being solved. However, for doing so and getting rid of confusions while solving. Students are advised to practice these as much as possible.

For doing so we have given the PDF that has a bunch of MCQs questions based on case based, assertion, important formulas, etc. All the Multiple Choice problems are given with detailed explanations.

CBSE Class 10th Case study Questions

Recently CBSE Board has the exam pattern and included case study questions to make the final paper a little easier. However, Many students are nervous after hearing about the case based questions. They should not be nervous because case study are easy and given in the board papers to ease the Class 10th board exam papers. However to answer them a thorough understanding of the basic concepts are important. For which students can refer to the NCERT textbook.

Basically, case study are the types of questions which are developed from the given data. In these types of problems, a paragraph or passage is given followed by the 5 questions that are given to answer . These types of problems are generally easy to answer because the data are given in the passage and students have to just analyse and find those data to answer the questions.

CBSE Class 10th Assertion Reasoning Questions

These types of questions are solved by reading the statement, and given reason. Sometimes these types of problems can make students confused. To understand the assertion and reason, students need to know that there will be one statement that is known as assertion and another one will be the reason, which is supposed to be the reason for the given statement. However, it is students duty to determine whether the statement and reason are correct or not. If both are correct then it becomes important to check, does reason support the statement? 

Moreover, to solve the problem they need to look at the given options and then answer them.

CBSE Class 10 Maths Case Based MCQ

CBSE Class 10 Maths Case Based MCQ are either Multiple Choice Questions or assertion reasons. To solve such types of problems it is ideal to use elimination methods. Doing so will save time and answering the questions will be much easier. Students preparing for the board exams should definitely solve these types of problems on a daily basis.

Also, the CBSE Class 10 Maths MCQ Based Questions are provided to us to download in PDF file format. All are developed as per the latest syllabus of CBSE Class Xth.

Class 10th Mathematics Multiple Choice Questions

Class 10 Mathematics Multiple Choice Questions for all the chapters helps students to quickly revise their learnings, and complete their syllabus multiple times. MCQs are in the form of objective types of questions whose 4 different options are given and one of them is a true answer to that problem. Such types of problems also aid in self assessment.

Case Study Based Questions of class 10th Maths are in the form of passage. In these types of questions the paragraphs are given and students need to find out the given data from the paragraph to answer the questions. The problems are generally in Multiple Choice Questions.

The Best Class 10 Maths Case Study Questions are available on Selfstudys.com. Click here to download for free.

To solve Class 10 Maths Case Studies Questions you need to read the passage and questions very carefully. Once you are done with reading you can begin to solve the questions one by one. While solving the problems you have to look at the data and clues mentioned in the passage.

In Class 10 Mathematics the assertion and reasoning questions are a kind of Multiple Choice Questions where a statement is given and a reason is given for that individual statement. Now, to answer the questions you need to verify the statement (assertion) and reason too. If both are true then the last step is to see whether the given reason support=rts the statement or not.

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NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

• Exercise 3.1
• Exercise 3.2
• Exercise 3.3
• Exercise 3.4
• Exercise 3.5
• Exercise 3.6
• Exercise 3.7

NCERT Solutions for Class 10 Maths Chapters:

How many exercises in chapter 3 pair of linear equations in two variables, at a certain time in a deer park, the number of heads and the number of legs of deer and human visitors were counted and it was found there were 39 heads & 132 legs. find the number of deer and human visitors in the park., what is graphical method of solution of a pair of linear equations, when the son will be as old as the father today their ages will add up to 126 years. when the father was old as the son is today, their ages add upto 38 years. find their present ages., contact form.

• Class 10 Maths MCQs
• Chapter 3 Pair Of Linear Equations In Two Variables

Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQs

Class 10 Maths MCQs for Chapter 3 (Pair of Linear Equations in Two Variables) are provided here online with answers. These multiple-choice questions will help students to score good marks in the board exam. These objective questions are prepared as per the latest CBSE syllabus (2022-2023) and NCERT textbook. The MCQs for Class 10 Maths Chapter 3 are prepared by our subject experts as per the latest exam pattern. Practising these questions will help them to develop problem-solving skills. To get chapter-wise MCQs, click here.  Also, download the PDF to get extra MCQs questions for practice.

Class 10 Maths MCQs for Pair of Linear Equations in Two Variables

Class 10 Maths exam datasheet is been released by the CBSE board. It is time for students to revise the chapters for the board exam. Students are required to solve these questions here and choose the appropriate answer for them. They can verify their answers with the given answers here. Get important questions for class 10 Maths here at BYJU’S.

Click here to download the PDF of additional MCQs for Practice on Pair of Linear Equations in Two Variables, Chapter of Class 10 Maths along with answer key:

Download PDF

Students can also get access to Pair of Linear Equations in Two Variables Class 10 Notes here.

Below are the MCQs for Chapter 3

1. The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have:

(a) Unique solution

(b) Exactly two solutions

(c) Infinitely many solutions

(d) No solution

Answer: (c) Infinitely many solutions

Explanation:

a 1 /a 2 = 1/-4

b 1 /b 2 = 2/-8 = 1/-4

c 1 /c 2 = -5/20 = -¼

This shows:

a 1 /a 2 = b 1 /b 2 = c 1 /c 2

Therefore, the pair of equations has infinitely many solutions.

2. If a pair of linear equations is consistent, then the lines are:

(a) Parallel

(b) Always coincident

(c) Always intersecting

(d) Intersecting or coincident

Answer: (d) Intersecting or coincident

Explanation: Because the two lines definitely have a solution.

3. The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have

Answer: (d) No solution

Explanation: Given, 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0

a 1 /a 2 = 9/18 = 1/2

b 1 /b 2 = 3/6 = 1/2

c 1 /c 2 = 12/26 = 6/13

Since, a 1 /a 2 = b 1 /b 2 ≠ c 1 /c 2

So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.

4. If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then what is the value of k?

Answer: (b) 15/4

Explanation: The condition for parallel lines is:

a 1 /a 2 = b 1 /b 2 ≠ c 1 /c 2

Hence, 3/2 = 2k/5

5. If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:

(a) -6x+10y-4=0

(b) 6x-10y-4=0

(c) 6x+10y-4=0

(d) -6x+10y+4=0

Answer: (a) -6x+10y-4=0

Explanation: The condition for dependent linear equations is:

For option a,

a 1 /a 2 = b 1 /b 2 = c 1 /c 2 = ½

6.The solution of the equations x-y=2 and x+y=4 is:

(a) 3 and 1

(b) 4 and 3

(c) 5 and 1

(d) -1 and -3

Answer:  (a) 3 and 1

Explanation: x-y =2

Substituting the value of x in the second equation we get;

Now putting the value of y, we get;

Hence, the solutions are x=3 and y=1.

7. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:

Answer: (c) 5/12

Explanation: Let the fraction be x/y

So, as per the question given,

(x -1)/y = 1/3 => 3x – y = 3…………………(1)

x/(y + 8) = 1/4 => 4x –y =8 ………………..(2)

Subtracting equation (1) from (2), we get

x = 5 ………………………………………….(3)

Using this value in equation (2), we get,

4×5 – y = 8

Therefore, the fraction is 5/12.

8. The solution of 4/x+3y=14 and 3/x-4y=23 is:

(a) ⅕ and -2

(b) ⅓ and ½

(c) 3 and ½

(d) 2 and ⅓

Answer: (a) ⅕ and -2

Explanation: Let 1/x = m

4m + 3y = 14

3m – 4y = 23

By cross multiplication we get;

m/(-69-56) = y/(-42-(-92)) = 1/(-16-9)

m/-125=y/50=-1/25

m/-125 = -1/25 and y/50=-1/25

m=5 and y=-2

m=1/x or x=1/m = ⅕

9. Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Her speed of rowing in still water and the speed of the current is:

(a) 6km/hr and 3km/hr

(b) 7km/hr and 4km/hr

(c) 6km/hr and 4km/hr

(d) 10km/hr and 6km/hr

Answer: (c) 6km/hr and 4km/hr

Explanation: Let, Speed of Ritu in still water = x km/hr

Speed of Stream = y km/hr

Now, speed of Ritu, during,

Downstream = x + y km/h

Upstream = x – y km/h

As per the question given,

2(x+y) = 20

Or x + y = 10……………………….(1)

And, 2(x-y) = 4

Or x – y = 2………………………(2)

Adding both the equations, we get,

Putting the value of x in eq.1, we get,

Speed of Ritu is still water = 6 km/hr

Speed of Stream = 4 km/hr

10. The angles of cyclic quadrilaterals ABCD are: A = (6x+10), B=(5x)°, C = (x+y)° and D=(3y-10)°. The value of x and y is:

(a) x=20° and y = 10°

(b) x=20° and y = 30°

(c) x=44° and y=15°

(d) x=15° and y=15°

Answer: (b) x=20° and y = 30°

Explanation: We know, in cyclic quadrilaterals, the sum of the opposite angles are 180°.

A + C = 180°

6x+10+x+y=180 =>7x+y=170°

And B+D=180°

5x+3y-10=180 =>5x+3y=190°

By solving the above two equations we get;

x=20° and y = 30°.

11. The pair of equations x = a and y = b graphically represents lines which are

(a) parallel 

(b) intersecting at (b, a)

(c) coincident 

(d) intersecting at (a, b)

Answer: (d) intersecting at (a, b)

The pair of equations x = a and y = b graphically represents lines which are intersecting at (a, b).

12. The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has

(a) one solution 

(b) two solutions 

(c) infinitely many solutions

(d) no solution

Answer: (c) infinitely many solutions

The given pair of equations are 5x – 15y = 8 and 3x – 9y = 24/5.

Comparing with the standard form,

a 1  = 5, b 1  = -15, c 1  = -8

a 2  = 3, b 2  = -9, c 2  = -24/5

a 1 /a 2 = 5/3

b 1 /b 2  = -15/-9 = 5/3

c 1 /c 2  = -8/(-24/5) = 5/3

Thus, a 1 /a 2  = b 1 /b 2  = c 1 /c 2

Hence, the given pair of equations has infinitely many solutions.

13. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have

(a) a unique solution 

(b) exactly two solutions

(c) infinitely many solutions 

Answer: (d) no solution

Given pair of equations are x + 2y + 5 = 0 and –3x – 6y + 1 = 0.

a 1  = 1, b 1  = 2, c 1  = 5

a 2  = -3, b 2  = -6, c 2  = 1

a 1 /a 2  = -1/3

b 1 /b 2  = 2/-6 = -1/3

c 1 /c 2  = 5/1

Thus, a 1 /a 2  = b 1 /b 2  ≠ c 1 /c 2

Hence, the given pair of equations has no solution.

14. The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is

(d) no value

Answer: (d) no value

Given pair of equations are cx – y = 2 and 6x – 2y = 3.

a 1  = c, b 1  = -1, c 1  = -2

a 2  = 6, b 2  = -2, c 2  = -3

a 1 /a 2  = c/6

b 1 /b 2  = -1/-2 = 1/2

c 1 /c 2  = -2/-3 = ⅔

Condition for having infinitely many solutions is

a 1 /a 2  = b 1 /b 2  = c 1 /c 2

c/6 = ½ = ⅔

Therefore, c = 3 and c = 4

Here, c has different values.

Hence, for no value of c the pair of equations will have infinitely many solutions.

15. If the lines representing the pair of linear equations a 1 x + b 1 y + c 1  = 0 and a 2 x + b 2 y + c 2  = 0 are coincident, then

(a) a 1 /a 2  = b 1 /b 2

(b) a 1 /a 2  = b 1 /b 2  = c 1 /c 2

(c) a 1 /a 2  ≠ b 1 /b 2

(d) a 1 /a 2  = b 1 /b 2  ≠ c 1 /c 2

Answer: (b) a 1 /a 2  = b 1 /b 2  = c 1 /c 2

If the lines representing the pair of linear equations a 1 x + b 1 y + c 1  = 0 and a 2 x + b 2 y + c 2  = 0 are coincident, then a 1 /a 2  = b 1 /b 2  = c 1 /c 2 .

16. A pair of linear equations which has a unique solution x = 2, y = -3 is

(a) x + y = -1; 2x – 3y = -5

(b) 2x + 5y = -11; 4x + 10y = -22

(c) 2x – y = 1; 3x + 2y = 0

(d) x – 4y – 14 = 0; 5x – y – 13 = 0

Answer: (b) 2x + 5y = -11; 4x + 10y = -22

If x = 2, y = -3 is a unique solution of any pair of equations, then these values must satisfy that pair of equations.

By verifying the options, option (b) satisfies the given values.

LHS = 2x + 5y = 2(2) + 5(- 3) = 4 – 15 = -11 = RHS

LHS = 4x + 10y = 4(2) + 10(- 3)= 8 – 30 = -22 = RHS

17. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively

(a) 4 and 24 

(b) 5 and 30

(c) 6 and 36 

(d) 3 and 24

Answer: (c) 6 and 36

Let x years be the present age of father and y years be the present age of son. 

According to the given,

(x + 4) = 4(y + 4) 

x + 4 = 4y + 16 

x- 4y + 4 – 16 = 0

x – 4y – 12 = 0….(i) 

Also, x = 6y….(ii) 

From (i) and (ii),

6y – 4y – 12 = 0 

Substituting y = 6 in (ii),

x = 6(6) = 36

18. If the pair of linear equations has a unique solution, then the lines representing these equations will 

(a) coincide

(b) intersect at one point

(c) parallel to each other

(d) parallel to x-axis

Answer: (b) intersect at one point

If the pair of linear equations has a unique solution, then the lines representing these equations will intersect at one point.

19. Which of the following method(s) is/are used to find the solution of a pair of linear equations algebraically?

(a) Substitution Method

(b) Elimination Method

(c) Cross- multiplication Method

(d) All the above

Answer: (d) All the above

The methods used to find the solution of a pair of linear equations algebraically are:

Substitution Method

Elimination Method

Cross- multiplication Method

20. The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15 will be

(a) parallel lines

(b) coincident lines

(c) intersecting lines

(d) perpendicular lines

Answer: (a) parallel lines

Given pair of equations are 4x + 3y – 1 = 5 and 12x + 9y = 15.

a 1  = 4, b 1  = 3, c 1  = -6

a 2  = 12, b 2  = 9, c 2  = -15

a 1 /a 2  = 4/12 = 1/3

b 1 /b 2  = 3/9 = 1/3

c 1 /c 2  = -6/-15 = 2/5

That means, the lines representing the given pair of equations are parallel to each other.

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CBSE Case Study Questions for Class 10 Maths Linear Equations in Two Variables Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Linear Equations in Two Variables  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

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CBSE Case Study Questions for Class 10 Maths Linear Equations in Two Variables PDF

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