Question

Find the values of a and b for which of the following system of equation has infinitely many solutions
(2a-1)x-3y=5
3x+(b-2)y=3​

Answer 1

(2a - 1)x - 3y = 5 ; 3x + ( b - 2)y = 3

On comparing,

a1 = 2a - 1 ; a2 = 3

b1 = -3 ; b2 = b - 2

c1 = 5 ; c2 = 3

For Infinitely many solutions, the lines must coincide.

So,

==> a1/a2 = b1/b2 = c1/c2

a1/a2 = c1/c2 ; b1/b2 = c1/c2

(2a - 1) / 3 = 5/3 ; -3/ (b - 2) = 5/3

2a - 1 = 5 ; 5b - 10 = -9

2a = 6 ; 5b = 1

a = 3 ; b = 1/5

Hence, for infinitely many solutions of a is 3 and value of b is 1/5