System

The system is equivalent to $\begin{cases} 2x + ky &=& 9\\ kx + 3y &=& 13 \end{cases}$.

As long as the lines represented by the equations are not parallel, the system would have a unique solution.

$-\dfrac2k \neq -\dfrac k3\\ k^2 \neq 6\\ k \neq \pm \sqrt 6$

For $k \neq \sqrt 6$ and $k \neq -\sqrt 6$, the system has a unique solution.