Question

Find the value of $k$ for which each of the following systems of equations have infinitely many solution:
$8x+5y=9$
$kx+10y=18$

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)

$\Rightarrow \frac{8}{k}=\frac{5}{10}=\frac{9}{18}$

$\Rightarrow k=16$