2x+y-z=-3,3x+2y+z=2,x-5y+2z=17
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2x+y-z=-3,3x+2y+z=2,x-5y+2z=17
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快 快 我感激不尽!
![2x+y-z=-3,3x+2y+z=2,x-5y+2z=17](/uploads/image/z/17024683-67-3.jpg?t=2x%2By-z%3D-3%2C3x%2B2y%2Bz%3D2%2Cx-5y%2B2z%3D17)
2x+y-z=-3 (1)
3x+2y+z=2 (2)
x-5y+2z=17 (3)
(1)+(2)得
5x+3y=-1 (4)
(1)×2+(3)得
5x-3y=11 (5)
(4)+(5)得
10x=10
∴x=1
把x=1代入(4)得
y=-2
把x=1,y=-2代入(1)得
2-2-z=-3
∴z=3
∴方程组的解是
x=1
y=-2
z=3
3x+2y+z=2 (2)
x-5y+2z=17 (3)
(1)+(2)得
5x+3y=-1 (4)
(1)×2+(3)得
5x-3y=11 (5)
(4)+(5)得
10x=10
∴x=1
把x=1代入(4)得
y=-2
把x=1,y=-2代入(1)得
2-2-z=-3
∴z=3
∴方程组的解是
x=1
y=-2
z=3
试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y)
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x+2y+4z=17 2x+y+z=7 3x+y+2z=11
2x-y+2z=-17 3x+y-3z=-4 x+y+z=6
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解方程组{z=x+y 3x-2y-2z=-5 2x+y-z=3