Solution:

The given system of equations is

kx + 2y – 5 = 0

3x + y – 1 = 0

The above equations are of the form

a₁ x + b₁ y − c₁ = 0

a₂ x + b₂ y − c₂ = 0

Here, a₁ = k, b₁ = 2, c₁ = −5

a₂ = 3, b₂ = 1, c₂ = -1

So, according to the question,

For a unique solution, the condition is

a₁ / a₂ ≠ b₁ / b₂

k/3 ≠ 2/1

⇒ k ≠ 6

Hence, the given system of equations will have a unique solution for all real values of k other than 6.