Question

Find the value of $k$ for which each of the following systems of equations have infinitely many solution:
$4x+5y=3$
$kx+15y=9$

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)

$\Rightarrow \frac{4}{k}=\frac{5}{15}=\frac{3}{9}$

$\Rightarrow k=12$