Question

Find the value of $k$ for which each of the following systems of equations have infinitely many solutions.
$2x+3y-5=0$
$6x+ky-15=0$

Answer 1

For the system to have infinitely many solutions, lines must coincide each other

$\Rightarrow$ratio of respective coefficients must be equal (x, y and constant coefficients)

$\Rightarrow \frac{2}{6}=\frac{3}{k}=\frac{5}{15}$

$\Rightarrow k=9$