解:$\begin{cases} 3x - 2y + z = 5 ① \\ 2x + y - z = 6 ② \\ x - y + z = 0 ③ \end{cases}$
①+②得:$5x - y = 11$ ④
②+③得:$3x = 6,$解得$x = 2$
将$x = 2$代入④得:$5×2 - y = 11,$解得$y = -1$
将$x = 2,$$y = -1$代入③得:$2 - (-1) + z = 0,$解得$z = -3$
所以方程组的解为$\begin{cases} x = 2 \\ y = -1 \\ z = -3 \end{cases}$