x+y-z=0 x+2y-z=3 2x-3y+2z=5

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x+y-z=0x+2y-z=32x-3y+2z=5x+y-z=0x+2y-z=32x-3y+2z=5x+y-z=0x+2y-z=32x-3y+2z=5x+y-z=01x+2y-z=322x-3y+2z

x+y-z=0 x+2y-z=3 2x-3y+2z=5
x+y-z=0 x+2y-z=3 2x-3y+2z=5

x+y-z=0 x+2y-z=3 2x-3y+2z=5
x+y-z=0 1
x+2y-z=3 2
2x-3y+2z=5 3
2-1式得y=3
将y=3代入2、3得
x-z=-3 4
x+z=7 5
4+5式得2x=4 解得x=2 y=5
综合得x=2 y=3 z=5

X=2,Y=3;Z=5

首先这是一个三元一次方程组:
x+y-z=0 ①
x+2y-z=3 ②
2x-3y+2z=5 ③
②-①: y=3
将 y=3 带入 ①和③:x-z=-3 ④
2x+2z=14 ⑤
④×2+⑤: x=2
将 x=2,y=3 带入①:z=5
所以 x=2,y=3,z=5

由x+y-z=0
得z=x+y
带入方程 x+2y-z=3
得y=3
将z=x+y带入2x-3y+2z=5
得x=2
将x=2,y=3带入x+y-z=0中,得z=5