Systems of Equations · Hard problem

Write the system as $A\mathbf{v} = \mathbf{b}$ with $A = \left[\begin{matrix}-2 & 2\\2 & 6\end{matrix}\right]$ and $\mathbf{b} = \left[\begin{matrix}6\\50\end{matrix}\right]$. Find $\det A$, and then $x$ and $y$.