Question

Find the value of $k$ for which following system of equations has a unique solution:
$4x-5y=k$
$2x-3y=12$

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

$\Rightarrow \frac{4}{2}\ne \frac{5}{3}$

$\Rightarrow$it is independent of k i.e, for all values of k, lines will intersect

$\Rightarrow k\in (-\infty ,\infty )$