Question

For what value of $k$, the pair of equations $3x+4y+2=0$ and $9x+12y+k=0$ represent co-incident lines.

Answer 1

For two lines to be co-incident,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

So, $\frac{3}{9}=\frac{4}{12}=\frac{2}{k}$

or, $\frac{2}{k}=\frac{1}{3}$

or, $k=6$