Question

解方程组：{2x+y+z x+2y+z x+y+2z 求出x、y、z

Answer 1

解：
2x+y+z=2
(1)
x+2y+z=4
(2)
x+y+2z=6
(3)
由(1)-(2)
得
x-y
=-2
(1)*2-(3)得
3x+y
=
-2
由以上两式相加得
4x=-4
得x=-1
所以
y
=
2-1
=1
z
=
3
所以
x=-1
y=1
z=3

Answer 2

完整题目应该是2x+y+z=17,x+2y+Z=18,x+y+2z=21
2X+Y+Z+X+2Y+Z=17+18得3X+3Y+2Z=35即3（X+Y）+2Z=35由X+Y+2Z=21得X+Y=21-2Z所以3（21-2Z）+2Z=35解得Z=7，所以X+Y=7即X=7-Y代入X+2Y+Z=18有7-Y+2Y+7=18，得Y=4X=7-Y=7-4=3所以X=3，Y=4，Z=7

Answer 3

1式2式3式加起来除以4，然后用1，2，3式减去它