Question

The system of linear equations 2x + 2y = 5, 5x + ky = 9 has a unique solution if

(a) k ≠ 5

(b) k = 0

(c) k ≠ –1

(d) k ≠ 2

Answer 1

Correct option is (a) k ≠ 5

The given system of equations can be written in the matrix form as:

Now there will be a unique solution for AX = B if |A| ≠ 0

i.e, 2k – 10 ≠ 0

⇒ k ≠ 5