Question

Find value of k such that equations -x + 3y - 3 = 0 and -3x + ky - 9 = 0, represents coincident lines.

Answer 1

For two lines $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ to be coincident,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\\ \Rightarrow \frac{-1}{-3}=\frac{3}{k}=\frac{-3}{-9}\\ \Rightarrow k=9$