4x-y+z=25 ①
6x-z+2y=22②
x+3y+z=-2 ③
①+②
10x+y=47 ④
②+③
7x+5y=20 ⑤
④×5-⑤
50x+5y-(7x+5y)=235-20
43x=215
x=5
将x=5代入④
y=47-10x=47-50=-3
将x=5,y=-3代入③
z=-2-x-3y=-2-5+9=2
方程组的解为：x=5,y=-3,z=2.