SSC CGL 2024 PYQ — Question 73

The correct answer is option 2 i.e. -1/4

x + 2Ky - 8 = 0

⇒ x + 2Ky = 8   .....(1)

2x - y - 16 = 0

⇒ 2x - y = 16   .....(2)

If a₁x + b₁y = c₁ and a₂x + b₂y = c₂ then (a₁/a₂) = (b₁/b₂) = (c₁/c₂) [Infinite solutions]

Here, a₁ = 1, b₁ = 2K, c₁ = 8 and a₂ = 2, b₂ = -1, c₂ = 16

So, 1/2 = (2K)/(-1) = 8/16

Then, 1/2 = (2K)/(-1)

K = -1/4

Let's verify if this value of K satisfies the third ratio,

(2K)/(-1) = 8/16

(-1/2)/(-1) = 1/2

1/2 = 1/2

Therefore, the value of K for which the system has an infinite number of solutions is -1/4.