$\left\{\begin{array} { l } 2x+y=1 \\ 3x-2y=12\end{array} \right.$
$\left\{\begin{array} { l } y=1-2x \\ 3x-2y=12\end{array} \right.$
$3x-2\left( 1-2x \right)=12$
$x=2$
$y=1-2 \times 2$
$y=-3$
$\left( x, y\right)=\left( 2, -3\right)$
$\left\{\begin{array} { l } 2 \times 2+\left( -3 \right)=1 \\ 3 \times 2-2 \times \left( -3 \right)=12\end{array} \right.$
$\left\{\begin{array} { l } 1=1 \\ 12=12\end{array} \right.$
$\left( x, y\right)=\left( 2, -3\right)$