解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.

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解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.
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解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.
解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.
解下列三元一次方程组.
(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.

解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.解下列三元一次方程组.(1)2x+2y+z=4,2x+y+2z=7,x+2y+2z=-6.
2x+2y+z=4……①,2x+y+2z=7……②,x+2y+2z=-6……③
①×2-②得:2x+3y=1……④
②-③得:x-y=13……⑤
⑤×3+④得:5x=40 x=8
代人⑤得:8-y=13 y=-5
代人①得:16-10+z=4 z=-2
∴{x=8 y=-5 z=-2

(1)2x+2y+z=4两边同时×2得(4)
(2)2x+y+2z=7与(3)相减得(6)
(3)x+2y+2z=-6
(4)4x+4y+2z=8(与(3)相减得(5)
(5)3x+2y=14
(6)x-y=13---- x=13+y 代入到(5)
3(13+y)+2y=14
39+3y+2y=14
5y=-25
y=-5
x=8
z=4-2x-2y=4-16+10=-2

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一式减二式得y-z=-3
三式乘以2得四式2x+4y+4z=-12
四式减二式得3y+2z=-19
解关于y 和z的二元一次方程的y=-5,z=-2
代入三式得x=8

z=4_2x_2y