Find the value of k for which each of the following systems of equations has a unique solution:

x - ky = 2, 3x + 2y + 5 = 0.

Given: x - ky = 2 – eq 1

3x + 2y + 5 = 0 – eq 2

Here,

a₁ = 1, b₁ = - k, c₁ = - 2

a₂ = 3, b₂ = 2, c₂ = 5

Given systems of equations has a unique solution

∴

2 ≠ - 3k

- 3k ≠2