Solve system of linear equations, using matrix method.

The given system of equations can be written in the form of AX = B, where

$A=\left[\begin{array}{ll}5 & 2 \\ 3 & 2\end{array}\right], X=\left[\begin{array}{l}x \\ y\end{array}\right]$ and $B=\left[\begin{array}{l}3 \\ 5\end{array}\right]$

Now,

$|A|=10-6=4 \neq 0$

Thus, A is non-singular. Therefore, its inverse exists.