$\left\{\begin{array} { l } -7x+y=-19 \\ -2x+3y=-19\end{array} \right.$
$\left\{\begin{array} { l } y=-19+7x \\ -2x+3y=-19\end{array} \right.$
$-2x+3\left( -19+7x \right)=-19$
$x=2$
$y=-19+7 \times 2$
$y=-5$
$\left( x, y\right)=\left( 2, -5\right)$
$\left\{\begin{array} { l } -7 \times 2+\left( -5 \right)=-19 \\ -2 \times 2+3 \times \left( -5 \right)=-19\end{array} \right.$
$\left\{\begin{array} { l } -19=-19 \\ -19=-19\end{array} \right.$
$\left( x, y\right)=\left( 2, -5\right)$