Question

Find the value of $k$ for which the system
$kx+2y=5$
$3x+y=1$
has (i) a unique solution and (ii) no solution.

Answer 1

(ii) For no solution, lines must be parallel

$\Rightarrow$ratio of respective x and y coefficients must be equal

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

$\Rightarrow k=6$

(i) For unique solution, lines should intersect each other

$\Rightarrow k\ne 6$

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