Question

If the system of equations

2x + 3y = 7

2ax + (a + b)y = 28

has infinitely many solutions, then the values of a and b respectively are ......

(A) 2,5

(B) 5, 8

(C) 4, 8

(D) 3, 6

Answer 1

The correct option is: (C) 4, 8

Explanation:

Given equations are

2x + 3y = 7 and 2ax + (a + b)y = 28

For infinitely many solutions, we have

Taking first two members, we get 2a + 2b = 6a

=> 4a = 2b + 2a = b          .....(1)

Also, 2/2a = 7/28 => a = 4             .....(2)

From (1) and (2), we have

2(4) = b 

=> b = 8