已知X+2Y-Z=8,且2X-Y+Z=18.则8X+Y+Z=70,为什么＝70?

X+2Y-Z=8
2X-Y+Z=18
设m(X+2Y-Z)+n(2X-Y+Z)=8X+Y+Z
m+2n=8
2m-n=1
-m+n=1
m=2
n=3
8X+Y+Z=m(X+2Y-Z)+n(2X-Y+Z)=m*8+n*18=2*8+3*18=70

8X+Y+Z=2(X+2Y-Z)+3(2X-Y+Z)=2*8+3*18=70

X+2Y-Z=8---等式一
2X-Y+Z=18---等式二
等式一+等式二---3X+Y=26---等式三
等式三*2+等式二=6X+2Y+2X-Y+Z=8X+Y+Z=26*2+18=70

（X+2Y-Z）+（2X-Y+Z）=8+18=26=3X+2Y
6X+2Y=52
（6X+2Y）+（2X-Y+Z）=8X+Y+Z=70

x+2y-z=8.1
2x+y+z=18.2
1式+2式得3x+y=26.3
3式左右乘2得6x+2y=52.4
4式+2式 得 ;8x+y+z=70