We observe that this matrix equation is in the standard form $\bfA \bfx = \bfb$, where $\bfA = \begin{pmatrix}2 & 3 \\ 10 & 16\end{pmatrix}$, $\bfx = \begin{pmatrix}x\\y\end{pmatrix}$, and $\bfb = \begin{pmatrix}1\\2\end{pmatrix}.$
The solution to the linear system is given by $\bfx = \bfA^{-1} \bfb$: $$ \bfx = \begin{pmatrix} 8 & -3/2 \\ -5 & 1 \end{pmatrix} \begin{pmatrix} 1 \\2 \end{pmatrix}$$