For what values of k is the system of equations kx + 3y = k - 2, 12x + ky = k inconsistent?

Given: kx + 3y = k - 2,

12x + ky = k

We know that the general form for a pair of linear equations in 2 variables x and y is a₁x + b₁y + c₁ = 0

and a₂x + b₂y + c₂ = 0.

Comparing with above equations,

we have a₁ = k, b₁ = 3, c₁ = - (k – 2); a₂ = 12, b₂ = k, c₂ = - k

For given equations to be inconsistent,

By cross multiplication, k² = 36

So, k = ±6

For k = ±6, the system of equations kx + 3y = k - 2, 12x + ky = k is inconsistent.