Question

For what value of $k$ the following system of equations will be inconsistent?
$4x+6y=11$
$2x+ky=7$

Answer 1

For the system to be inconsistent, lines must be parallel.

$\Rightarrow$ratio of respective ${}^{\prime }{x}^{\prime }$ and ${}^{\prime }{y}^{\prime }$ coefficients must be equal

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

$\Rightarrow k=12$