Question

Find the value of $k$ for which following system of equations has a unique solution:
$kx+2y=5$
$3x+y=1$

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

$\Rightarrow \frac{k}{3}\ne \frac{2}{1}$

$\Rightarrow k\ne 6$

$\Rightarrow k\in (-\infty ,\infty )-\left\{6\right\}$