# NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations

Download NCERT Solutions for class 10 Maths chapter 3 Pair of Linear Equations in Two Variables all exercise 3.7, 3.6, 3.5, 3.4, 3.3, 3.2 & 3.1 in English & Hindi medium in PDF. NCERT Solutions for class 10 Maths chapter 3 are available for CBSE Board, UP Board High School and other state Boards to download. Students can find Hindi medium solutions below in PDF. Get CBSE Syllabus 2019-20.

## NCERT Solutions Class 10 Maths Chapter 3

In the third chapter you will study about the Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. You will learn about solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Learn about the Simple situational problems. Simple problems on equations reducible to linear equations. It has 7 exercises to be solved. A worksheet has been given below to solve.

10 Maths Chapter 3 Solutions Exercise 3.1

Class 10 Maths Chapter 3 Solutions Exercise 3.2

Class 10 Maths Chapter 3 Solutions Exercise 3.3

Class 10 Maths Chapter 3 Solutions Exercise 3.4

Class 10 Maths Chapter 3 Solutions Exercise 3.5

Class 10 Maths Chapter 3 Solutions Exercise 3.6

Class 10 Maths Chapter 3 Solutions Exercise 3.7

### Maths Chapter 3 Solutions Hindi Medium

• प्रश्नावली 3.1 Solutions in Hindi
• प्रश्नावली 3.2 Solutions in Hindi
• प्रश्नावली 3.3 Solutions in Hindi
• प्रश्नावली 3.4 Solutions in Hindi
• प्रश्नावली 3.5 Solutions in Hindi
• प्रश्नावली 3.6 Solutions in Hindi
• प्रश्नावली 3.7 Solutions in Hindi

Read or study online 10th Maths Chapters Solutions – class 10 maths solutions chapter 3.

#### Questions for Practice

These questions are taken for the NCERT Solutions class 10 Maths chapter 3 for practice yourself.

1. Solve graphically the following pairs of linear equations:
(i) 2x – y = 4
3y – x = 3 Also, find the coordinates of the points where these lines intersect the 2 axes.)
(ii) 2x + 3y = 12
x – y = 1 Shade the region (area) between the 2 lines and x axis.
2. Find graphically the coordinates of the vertices of a triangle whose sides have the equations:
(i) y = x, y = 0 and 2x + 3y = 30 (iii) y = x, 3y = x and x + y = 8
(ii) 2y –x = 8, 5y – x = 14 and y – 2x = 1
3. Plot a graph for each of the following pairs of equations and shade the region bounded by the 2 lines and the x-axis.
(i) x – y + 1 = 0 (ii) 4x – 3y + 4 = 0 (iii) 2x + y = 6 (iv) x + y = 5
2x + y – 10 = 0 4x + 3y – 20 = 0 2x – y + 2 = 0 2x – y +2 =0
4. Solve the following pair of linear equations graphically: 3x + y – 11 = 0; x – y – 1 = 0
Shade the region bounded by these lines and the axis of y.
5. Solve each of the following pairs of linear equations graphically:
(i) 5x – 6y + 30 = 0 (ii) 3x – 4y + 6 = 0
5x + 4y – 20 = 0 3x + y – 9 = 0
6. Find the value of c for which the pair of equations : 2x + cy = 1; 3x + 5y = 7 will have
(i) a unique solution; (ii) no solution. Is there a value of c for which the system has infinite number of solutions?
7. Find the value of k for which the following pairs of equations have unique solutions:
(i) 7x – 2y = 3; 22x – ky = 8 (ii) 2x + ky = 1; 3x – 5y = 7 (iii) 2x + 3y – 5 = 0; kx – 6y – 8 = 0
8. For what value(s) of k will the pair of linear equations: kx + 3y = k – 3; 12x + ky = k have a unique
solution?
##### Chapter 3 Worksheet 2

These questions are taken from NCERT Solutions class 10 Maths chapter 3.

1. Last year 1 kg of tea and 3 kg of sugar together cost Rs 96. This year, the rates of tea increased by 15% and that of sugar by 10%. So the amount of tea and sugar now cost Rs. 108.60. Find the per kg rates of tea & sugar last year.
2. A boat goes 24 km upstream & 28 km downstream in 6 hours. In 6.5 hours, it can go 30 km upstream & 21 km downstream. Find the speed of stream and the speed of boat in still water.
3. A person invests some amount @ 12% S.I. and some other amount @ 10% S.I..He receives an annual interest of Rs.1300. But if he interchanges the amounts invested, he shall receive Rs.40 more as interest. How much has he invested at each rate?
4. If 1 is added to both the numerator and the denominator of a fraction, it becomes equal to
8/7. If, however, 1 is subtracted from both the numerator & denominator of the same fraction, it becomes equal to 6/7 . Find the fraction.
5. The age of a father 8 years back was 5 times that of his son. After 8 yrs, his age will be 8 yrs more than double the age of his son. Find their present ages.
6. There are some lotus flowers in a lake. If 1 butterfly sits on each flower, one butterfly is left behind. If 2 butterflies sit on each flower, 1 flower is left behind. What is the no. of flowers? What is the no. of butterflies?
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