$\left\{\begin{array} { l } -3x+2y=-6 \\ -5x+10y=30\end{array} \right.$

$\left[\begin{matrix} -3 & 2 \\ -5 & 10 \end{matrix}\right] \times \left[\begin{matrix} x \\ y \end{matrix}\right]=\left[\begin{matrix} -6 \\ 30 \end{matrix}\right]$

$A=\left[\begin{matrix} -3 & 2 \\ -5 & 10 \end{matrix}\right]$

${A}^{-1}=\left[\begin{matrix} -\frac{ 1 }{ 2 } & \frac{ 1 }{ 10 } \\ -\frac{ 1 }{ 4 } & \frac{ 3 }{ 20 } \end{matrix}\right]$

$\left[\begin{matrix} x \\ y \end{matrix}\right]=\left[\begin{matrix} -\frac{ 1 }{ 2 } & \frac{ 1 }{ 10 } \\ -\frac{ 1 }{ 4 } & \frac{ 3 }{ 20 } \end{matrix}\right] \times \left[\begin{matrix} -6 \\ 30 \end{matrix}\right]$

$\left[\begin{matrix} x \\ y \end{matrix}\right]=\left[\begin{matrix} 6 \\ 6 \end{matrix}\right]$

$\begin{array} { l }x=6,\\y=6\end{array}$

$\left( x, y\right)=\left( 6, 6\right)$

$\left\{\begin{array} { l } -3 \times 6+2 \times 6=-6 \\ -5 \times 6+10 \times 6=30\end{array} \right.$

$\left\{\begin{array} { l } -6=-6 \\ 30=30\end{array} \right.$

$\left( x, y\right)=\left( 6, 6\right)$