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.