$A = \left[ {\begin{array}{*{20}{c}}
  1&{ - 2} \\ 
  3&1 
\end{array}} \right]\;\; \Rightarrow \;\;|A|\; = 7$
${A^{ - 1}} = \frac{1}{7}\left[ {\begin{array}{*{20}{c}}
  1&2 \\ 
  { - 3}&1 
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
  {\frac{1}{7}}&{\frac{2}{7}} \\ 
  {\frac{{ - 3}}{7}}&{\frac{1}{7}} 
\end{array}} \right]$
$ \Rightarrow \;\;\left[ {\begin{array}{*{20}{c}}
  x \\ 
  y 
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
  {\frac{1}{7}}&{\frac{2}{7}} \\ 
  {\frac{{ - 3}}{7}}&{\frac{1}{7}} 
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
  4 \\ 
  5 
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
  2 \\ 
  { - 1} 
\end{array}} \right]\;\; \Rightarrow \;\;\left\{ {\begin{array}{*{20}{l}}
  {x = 2} \\ 
  {y =  - 1} 
\end{array}} \right.$