-3x 2y = -6; -5x 10y = 30



Answer to a math question -3x 2y = -6; -5x 10y = 30

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$\left\{\begin{array} { l } -3x+2y=-6 \\ -5x+10y=30\end{array} \right.$
$\left[\begin{matrix} -3 & 2 \\ -5 & 10 \end{matrix}\right] \times \left[\begin{matrix} x \\ y \end{matrix}\right]=\left[\begin{matrix} -6 \\ 30 \end{matrix}\right]$
$A=\left[\begin{matrix} -3 & 2 \\ -5 & 10 \end{matrix}\right]$
${A}^{-1}=\left[\begin{matrix} -\frac{ 1 }{ 2 } & \frac{ 1 }{ 10 } \\ -\frac{ 1 }{ 4 } & \frac{ 3 }{ 20 } \end{matrix}\right]$
$\left[\begin{matrix} x \\ y \end{matrix}\right]=\left[\begin{matrix} -\frac{ 1 }{ 2 } & \frac{ 1 }{ 10 } \\ -\frac{ 1 }{ 4 } & \frac{ 3 }{ 20 } \end{matrix}\right] \times \left[\begin{matrix} -6 \\ 30 \end{matrix}\right]$
$\left[\begin{matrix} x \\ y \end{matrix}\right]=\left[\begin{matrix} 6 \\ 6 \end{matrix}\right]$
$\begin{array} { l }x=6,\\y=6\end{array}$
$\left( x, y\right)=\left( 6, 6\right)$
$\left\{\begin{array} { l } -3 \times 6+2 \times 6=-6 \\ -5 \times 6+10 \times 6=30\end{array} \right.$
$\left\{\begin{array} { l } -6=-6 \\ 30=30\end{array} \right.$
$\left( x, y\right)=\left( 6, 6\right)$

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