{x+2y+z=4,x+y+2z=-1,2x+y+z=1

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{x+2y+z=4,x+y+2z=-1,2x+y+z=1
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{x+2y+z=4,x+y+2z=-1,2x+y+z=1
{x+2y+z=4,x+y+2z=-1,2x+y+z=1

{x+2y+z=4,x+y+2z=-1,2x+y+z=1
x+2y+z=4(1),x+y+2z=-1(2),2x+y+z=1(3)
三式相加:4x+4y+4z=4,∴x+y+z=1(4)
(1)-(4)得y=3
(2)-(4)得z=-2
(3)-(4)得x=0