Question

For what value of k do the equations kx – 2y = 3 and 3x + y = 5 represent two lines intersecting at a unique point?

Options

• k = 3

• k = –3

• k = 6

• all real values except –6

Answer 1

All real values except –6

Explanation:

For a unique intersecting point, we have `(a_1)/(a_2) ≠ (b_1)/(b_2)`.

∴ `k/3 ≠ (-2)/1`

⇒ k ≠ –6

Hence, all real values except –6.