Question

Find the value of $k$ for which following system of equations has a unique solution:
$x+2y=3$
$5x+ky+7=0$

Answer 1

For the system to have unique solution, lines must intersect each other

$\Rightarrow$it should be neither Parallel nor coincide each other

$\Rightarrow$ratio of respective coefficients must not be equal

$\Rightarrow \frac{1}{5}\ne \frac{2}{k}$

$\Rightarrow k\ne 10$

$\Rightarrow k\in (-\infty ,\infty )-\left\{10\right\}$