## Class ten Chapter 3 NCERT Maths Solutions

#### Chapter 3: Pair of Linear equations of two variables

**TEXTBOOK’S EXERCISE 3.5 **

**1. Which of the following pairs of linear equations has a unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.**

- X- 3y – 3 = 0, 3x – 9y- 2 =0
- 2x + y = 5, 3x -2y = 8
- 3x – 5y = 20, 6x – 10y= 40
- X- 3y -7 =0, 3x -3y-15=0

**Sol.
**(i)
Given equations are :

- Given equations are:

x-3y-3=0——-(i)

3x – 9y-2 =0——(2)

Therefore, the pair of linear equations is inconsistent. Hence, given equations has no solution.

Given equations are :

2x + y = 5

2x+y-5=0

3x + 2y = 8

3x +2y-8 = 0

∴ The given system of equations is consistent, that means equations have unique solution.

From equation (1) and equation (2), by cross-multiplication, we have

Hence, given equations have an infinite number of solutions.

(iv) Given equations are :

*x – *3*y – *7 = 0 …(1)

and 3*x *– 3*y *– 15 = 0

∴ Given equations have a unique solution.

From equation (1) and equation (2), we have

Hence , x = 4 and y = – 1.

**2. **(**i) For which values of a and b does the following pair of linear equations have an infinite number of solutions? **

**2x + 3y = 7; (a – b)x + (a + b)y = 3a + b – 2**

**(ii)For which value of k will the following pair of linear equations have no solution?**

**Sol. **(i)
Given equations are :

2*x *+ 3*y *= 7 …(1)

∴ System of equations have an infinite number of solutions.

9a + 3b-6 = 7a + 7b

2a-4b-6=0

a-2b-3=0———(4)

9b- 4 – 2b – 3=0

7b – 7 = 0

7b = 7

b= 1

Putting the value of
*a *in equation (4), we get

9b – 4-2b-3 = 0

7b -7 = 0

7b = 7

b= 1

Putting the value of *b *in equation (3), we get

a = 9×1-4=9-4=5

Hence, *a *= 5 and *b *= 1

Given equations are :

∵ System of equations have no solution