Question

Find the value (s) of k, if the following equations are consistent: kx + 3y + 4 = 0, x + ky + 3 = 0, 3x + 4y + 5 = 0

Answer 1

Given equations are
kx + 3y + 4 = 0
x + ky + 3 = 0
3x + 4y + 5 = 0
Since, these equations are consistent.

∴ `|("k", 3, 4),(1, "k", 3),(3, 4, 5)|` = 0

∴ k(5k – 12) – 3(5 –9) + 4(4 – 3k) = 0
∴ 5k² – 12k + 12 + 16 – 12k = 0
∴ 5k² – 24k + 28 = 0
∴ 5k² – 10k – 14k + 28 = 0
∴ 5k(k – 2) –14(k – 2) = 0
∴ (k – 2) (5k – 14) = 0
∴ k – 2 = 0 or 5k – 14 = 0
∴ k = 2 or k = `14/5`