方程组x-y-z=-1 3x+5y+7z=9 4x-y+2z=-1

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方程组x-y-z=-1 3x+5y+7z=9 4x-y+2z=-1
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方程组x-y-z=-1 3x+5y+7z=9 4x-y+2z=-1
方程组x-y-z=-1 3x+5y+7z=9 4x-y+2z=-1

方程组x-y-z=-1 3x+5y+7z=9 4x-y+2z=-1
x-y-z=-1 .1
3x+5y+7z=9 .2
4x-y+2z=-1 .3
1式得 x = y+z-1
代入 2 3式子

3y+3z-3 +5y+7z =9 8y+10z = 12 4y+5z = 6
4y+4z-4 -y +2z = -1 3y +6z = 3 y+2z =1
4-8z+5z = 6
3z = -2
z=-2/3
y = 1+4/3 = 7/3
x = 5/3-1 = 2/3
x y z 分别为 2/3 7/3 -2/3

(1)×7+(2)得
10x-2y=2
5x-y=1 (4)
(1)×2+(3)得
6x-3y=-3
2x-y=-1 (5)
(4)-(5)得
3x=2
∴ x=2/3
把x=2/3代入(5)得
y=7/3
把x=2/3,y=7/3代入(1)得
z=-2/3
...

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(1)×7+(2)得
10x-2y=2
5x-y=1 (4)
(1)×2+(3)得
6x-3y=-3
2x-y=-1 (5)
(4)-(5)得
3x=2
∴ x=2/3
把x=2/3代入(5)得
y=7/3
把x=2/3,y=7/3代入(1)得
z=-2/3
∴方程组的解是
x=2/3
y=7/3
z=-2/3

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