Systems of Equations · Hard problem

Write the system as $A\mathbf{v} = \mathbf{b}$ with $A = \left[\begin{matrix}5 & -3\\-5 & 5\end{matrix}\right]$ and $\mathbf{b} = \left[\begin{matrix}-23\\25\end{matrix}\right]$. Find $\det A$, and then $x$ and $y$.