已知2x+2y-4z=0,2x+4y+5z=0,求x+y+z/x-y+z的值

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已知2x+2y-4z=0,2x+4y+5z=0,求x+y+z/x-y+z的值

已知2x+2y-4z=0,2x+4y+5z=0,求x+y+z/x-y+z的值
已知2x+2y-4z=0,2x+4y+5z=0,求x+y+z/x-y+z的值

已知2x+2y-4z=0,2x+4y+5z=0,求x+y+z/x-y+z的值
本题不一定要算出x、y,也能解出.
(1)2x+2y-4z=0
(2)2x+4y+5z=0
(2)-(1):2y+9z=0 即2y=-9z
(1)÷2可得:x+y =2z
故x+y+z=3z
则x-y+z=(x+y+z)-2y=3z+9z=12z
易得x+y+z/x-y+z=3z/12z=1/4

x+y-2z=0 2x+4y+5z=0
x=6.5z,y=-4.5z
x+y+z/x-y+z 将x=6.5,y=-4.5代入得
原试
=1/4

2x+2y-4z=0,2x+4y+5z=0,可得:y= - 4.5z,x=6.5z
(x+y+z)/(x-y+z)=(6.5z-4.5z+z)/(6.5z+4.5z+z)=1/4