Question

Find the value of $k$ for which the following system of equations has no solution:
$3x-4y+7=0$
$kx+3y-5=0$

Answer 1

For the system of equations to have no solution, the lines must be parallel.

$\Rightarrow$The ratio of '$x$' and '$y$' coefficients must be equal.

$\Rightarrow \frac{3}{k}=\frac{-4}{3}$

$\Rightarrow k=\frac{-9}{4}$