{3x-y+z=4,2x+3y-z=12,x+y+z=6

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{3x-y+z=4,2x+3y-z=12,x+y+z=6{3x-y+z=4,2x+3y-z=12,x+y+z=6{3x-y+z=4,2x+3y-z=12,x+y+z=63x-y+z=4,(1)2x+3

{3x-y+z=4,2x+3y-z=12,x+y+z=6
{3x-y+z=4,2x+3y-z=12,x+y+z=6

{3x-y+z=4,2x+3y-z=12,x+y+z=6
3x-y+z=4,(1)
2x+3y-z=12,(2)
x+y+z=6 (3)
(1)+(2)得
5x+2y=16 (4)
(2)+(3)得
3x+4y=18 (5)
(4)*2-(5)得
7x=14
x=2
代入(4)得
y=3
把x、y的值代入(3)得
z=1