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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 – 3y – 7 = 0 …(1)

and 3x – 3y – 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 :

2x + 3y = 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

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