x-y+z=5 ①
2x+3y-2z=4 ②
3x-y+2z=3③
①×2+②
4x-2y+3y=10+4
4x+y=14
∴y=14-4x④
②+③
5x+2y=7⑤
代④入⑤
5x+2(14-4x)=7
5x+28-8x=7
3x=21
x=7
∴y=14-4×7=-14
∵z=5+y-x=5-14-7=-16
即：方程组的解为x=7,y=-14,z=-16