$A = \left[ {\begin{array}{*{20}{c}}
  3 \\ 
  2 
\end{array}\,\,\,\,\begin{array}{*{20}{c}}
  { - 5} \\ 
  1 
\end{array}} \right]\,\,,\,\,\left| A \right| = 3 + 10 = 13 \Rightarrow {A^{ - 1}} = \frac{1}{{13}}\left[ {\begin{array}{*{20}{c}}
  1 \\ 
  { - 2} 
\end{array}\,\,\,\begin{array}{*{20}{c}}
  5 \\ 
  3 
\end{array}} \right]\,\,\,,\,\,B = \left[ {\begin{array}{*{20}{c}}
  { - 1} \\ 
  8 
\end{array}} \right]$

$X = \left[ {\begin{array}{*{20}{c}}
  x \\ 
  y 
\end{array}} \right] = {A^{ - 1}} \times B = \frac{1}{{13}}\left[ {\begin{array}{*{20}{c}}
  1 \\ 
  { - 2} 
\end{array}\,\,\,\,\begin{array}{*{20}{c}}
  5 \\ 
  3 
\end{array}} \right] \times \left[ {\begin{array}{*{20}{c}}
  { - 1} \\ 
  8 
\end{array}} \right] = \frac{1}{{13}}\left[ {\begin{array}{*{20}{c}}
  { - 1 + 40} \\ 
  {2 + 24} 
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
  3 \\ 
  2 
\end{array}} \right] \Rightarrow x = 3\,,\,y = 2$