Question

Find the value (s) of k, if the following equations are consistent: 3x + y – 2 = 0, kx + 2y – 3 = 0 and 2x – y = 3

Answer 1

Given equations are
3x + y – 2 = 0
kx + 2y – 3 = 0
2x – y = 3 i.e. 2x – y – 3 = 0
Since, these equations are consistent.

`|(3, 1, -2),("k", 2, -3),(2, -1, -3)|` = 0

∴ 3(–6 – 3) –1(–3k + 6) – 2(–k – 4) = 0
∴ 3(–9) – 1(–3k + 6) – 2(– k – 4) = 0
∴ –27 + 3k – 6 + 2k + 8 = 0
∴ 5k – 25 = 0

∴ k = `25/5`
= 5