SSC CGL 2024 PYQ — Question 58

The correct answer is option 3 i.e. a = 1,b = - 1.

Condition for infinitely many solutions is: If there are two equations, say;

a₁x + b₁y = c₁ and a₂x + b₂y = c₂

Then, ${a_1 \over a_2} = {b_1 \over b_2} = {c_1 \over c_2}$

According to the given question, the two equations are:

ax + by = 2

3x - (5 - 2a)y = 6

⇒ ${a \over 3} = {2 \over 6}$

⇒ 6a = 6

⇒ a = 1

Now, ${b \over -(5 - 2a)} = {2 \over 6}$

⇒ 6b = -2(5 - 2)

⇒ 6b = -6

⇒ b = -1

Hence the values of a and b to have infinitely many solutions are a = 1,b = - 1.