Q. 6

# 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.

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