2x-y+2z=6 3x+y-3z=-4 x+y+z=6

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2x-y+2z=6 3x+y-3z=-4 x+y+z=6
2x-y+2z=6 3x+y-3z=-4 x+y+z=6

2x-y+2z=6 3x+y-3z=-4 x+y+z=6
2x-y+2z=6 (1)
3x+y-3z=-4 (2)
x+y+z=6 (3)
(1)+(2)
5x-z=2 (4)
(1)+(3)
3x+3z=12
x+z=4 (5)
(4)+(5)
6x=6
x=1
z=4-x=3
y=2x+2z-6=2

X=1,Y=2,Z=3

(1)2x-y+2z=6
(2)3x+y-3z=-4
(3)x+y+z=6
(1)+(2),5x-z=2 (4)
(1)+(3),3x+3z=12,x+z=4 (5)
联立(4)(5),得
x=1,z=3,代入(1)得
y=2