SSC CGL 2024 PYQ — Question 58

The correct answer is option 3 i.e. a = 3, b = $-\frac {3}{2}$.

If a₁x + b₁y = c₁ and a₂x + b₂y = c₂

The given equations have infinitely solutions, if (a₁/a₂) = (b₁/b₂) = (c₁/c₂)

Here, 3x + y = 3   .....(1)

(a - b)x + (a + b)y = 3a + b - 3   .....(2)

So, 3/(a - b) = 1/(a + b) = 3/(3a + b - 3)

Then, 3/(a - b) = 1/(a + b)

⇒ 3a + 3b = a - b

⇒ 2a = -4b

⇒ a = -2b   .....(3)

Also, 3/(a - b) = 3/(3a + b - 3)

⇒ a - b = 3a + b - 3

⇒ -2a - 2b = -3

⇒ -2(-2b) - 2b = -3

⇒ 4b - 2b = -3

⇒ 2b = -3

⇒ b = -3/2

Putting b = -3/2 bin equation (3),

a = -2(-3/2) = 3

Therefore, the values are a = 3 and b = -3/2.