解方程组x-y+z=-1,2x+y-z=-1,3x-2y-2z=-9

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解方程组x-y+z=-1,2x+y-z=-1,3x-2y-2z=-9
解方程组x-y+z=-1,2x+y-z=-1,3x-2y-2z=-9

解方程组x-y+z=-1,2x+y-z=-1,3x-2y-2z=-9
x-y+z=-1 (1)
2x+y-z=-1 (2)
3x-2y-2z=-9 (3)
(1)+(2),得 3x=-2
x=-2/3 (4)
(4)代入(1),得
-y+z=-1/3 (5)
(4)代入(3),得
-2y-2z=-7
y+z=7/2 (6)
(5)+(6)得 z=19/12
(5)-(6)得 y=23/12
∴x=-2/3
y=23/12
z=19/12

X=-2/3,Y=23/12,Z=19/12
x-y+z=-1 (1)
2x+y-z=-1 (2)
3x-2y-2z=-9 (2)
(1)+(2)
3x=-2
x=-2/3
(2)*2+(3)
7x-4z=-11
z=19/12
x=-2/3,z=19/12代入(1)
-2/3-y+19/12=-1
Y=23/12