x+y=2 y+z=1 z+x=5
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x+y=2 y+z=1 z+x=5
x+y=2 y+z=1 z+x=5
x+y=2 y+z=1 z+x=5
三个方程相加得:2(x+y+z)=2+1+5,x+y+z=4
x+y+z=4式减一式得:z=2
同理的:x=3,y=-1
即:x=3,y=-1,z=2
x+y=2 .......(1)
y+z=1..........(2)
z+x=5 ........(3)
则(1)-(2)得:x-z=1......(4)
(3)+(4)得:2x=6
解得:x=3
把x=3代入(1)得:y=-1
把x=3代入(3)得:z=2
(1)x+y=2
(2) y+z=1
(3) z+x=5
(4)=x-z=1【(1)-(2)】
(4)+(3)得到 2x=6 x=3 y=-1 z=2
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