Question

Find k if kx+3y+1=0 and 2x+y+3=0 has unique solution

Answer 1

kx + 3y + 1 = 0

2x + y + 3 = 0

$a_{1} = k \: \: \: b_{1} = 3 \: \: \: c_{1} = 1 \\ a_{2} = 2 \: \: \: b_{2} = 1 \: \: \: c_{2} = 3$
For unique solution,
a1/a2 ≠ b1/b2
=>k/2 ≠ 3/1
=> k ≠ 3 × 2
=> k ≠ 6

Hope it'll help...