Question

Find the values of $k$ so that the pair of linear equations $kx-2y=3$ and $3x+y=5$ has a unique solution.

Answer 1

$\begin{array}{c}kx-2y=\mathrm{3.....}\left(1\right)\\ 3x+y=\mathrm{5.......}\left(2\right)\end{array}$

For unique solution

$\begin{array}{c}\Rightarrow \left|\begin{array}{cc}k& -2\\ 3& 1\end{array}\right|\ne 0\\ \Rightarrow k+6\ne 0\\ \Rightarrow k\ne -6\end{array}$

Hence, this is the answer.