Question

Find the value of k for which each of the following systems of equations have infinitely many solution:
$kx-2y+6=0$
$4x-3y+9=0$

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)

$\Rightarrow \frac{k}{4}=\frac{2}{3}=\frac{6}{9}$

$\Rightarrow k=\frac{8}{3}$