$\left\{ \begin{matrix} x + 2y - z = 3 \\ x - y + z = 2 \\ \end{matrix} \right.\ $ $\left\{ \begin{matrix} x + 2y = 3 + z \\ x - y = 2 - z \\ \end{matrix} \right.\ $

$W = \left| \begin{matrix} 1 & 2 \\ 1 & - 1 \\ \end{matrix} \right| = - 1 - 2 = - 3\ \neq 0$ $W_{x}\left| \begin{matrix} 3 + z & 2 \\ 2 - z & - 1 \\ \end{matrix} \right| = - 3 - z - 4 + 2z = z - 7$

$$W_{y}\left| \begin{matrix} 1 & 3 + z \\ 1 & 2 - z \\ \end{matrix} \right| = 2 - a - 3 - z = - 1 - 2z$$

$\left\{ \begin{matrix} x = z - 7 \\ y = - 1 - 2z \\ \end{matrix} \right.\ $ z − 7 + 1 + 2z = 2 − z → 4z = 8  → z = 2

$$\left\{ \begin{matrix} x = 2 - 7 = - 5 \\ y = - 1 - 4 = - 5 \\ \end{matrix} \right.\ $$