Question

$2x+3y-5=0$
$6x+ky-15=0$
The value of $k$ for which following system of equations have infinitely many solutions is ___

Answer 1

Condition for infinitely many solutions is $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{2}{6}=\frac{3}{k}\Rightarrow k=9$

When $k=9$, it represents two exactly same lines, so all the points coincide, thus giving infinitely many solutions.