Es ist

${\displaystyle {}x_{1}={\frac {\det {\begin{pmatrix}5&7\\2&3\end{pmatrix}}}{\det {\begin{pmatrix}3&7\\2&3\end{pmatrix}}}}=-{\frac {1}{5}}\,}$

und

${\displaystyle {}x_{2}={\frac {\det {\begin{pmatrix}3&5\\2&2\end{pmatrix}}}{\det {\begin{pmatrix}3&7\\2&3\end{pmatrix}}}}={\frac {-4}{-5}}={\frac {4}{5}}\,.}$