Question

If the pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0 has a unique solution for all real values of p except ______.

Answer 1

If the pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0 has a unique solution for all real values of p except –4.

Explanation:

For a unique solution the determinant must be nonzero: 2 × (–6) – p × 3 = –12 – 3p ≠ 0, which gives p ≠ –4. If p = –4 the lines become parallel (no unique intersection).