求解三元一次方程
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求解三元一次方程
![](http://img.wesiedu.com/upload/a/35/a3576ed4fcb758dc75bd9c0e056dd4aa.jpg)
![](http://img.wesiedu.com/upload/a/35/a3576ed4fcb758dc75bd9c0e056dd4aa.jpg)
![求解三元一次方程](/uploads/image/z/20109371-59-1.jpg?t=%E6%B1%82%E8%A7%A3%E4%B8%89%E5%85%83%E4%B8%80%E6%AC%A1%E6%96%B9%E7%A8%8B+%26nbsp%3B)
2x+3y+z=6①,x-y﹢2z=﹣1②,x+2y-z=5③
①+③,得3x+5y=11④,
②+③,得2x+y+z=4⑤,
⑤+③,得3x+3y=9⑥,
④-⑥得2y=2,即y=1⑦
将⑦代入⑥,得x=2⑧
将⑦,⑧代入⑤,得4+1+z=4,
∴z=﹣1,
∴x=1,y=2,z=﹣1
①+③,得3x+5y=11④,
②+③,得2x+y+z=4⑤,
⑤+③,得3x+3y=9⑥,
④-⑥得2y=2,即y=1⑦
将⑦代入⑥,得x=2⑧
将⑦,⑧代入⑤,得4+1+z=4,
∴z=﹣1,
∴x=1,y=2,z=﹣1