已知{3x-y+2z=14 4x-8y+z=7 求x+y+z的值

问题描述:

已知{3x-y+2z=14 4x-8y+z=7 求x+y+z的值


因为:3x-y+2z=14,4x-8y+z=7,
所以:3(x+y+z)-(4y+z)=14,4(x+y+z)-3(4y+z)=7
联立方程组,解得:x+y+z=36/5

3x-y+2z=14 ①
4x-8y+z=7 ②
∴①-2×②得 -5x+15y=0,即 x-3y=0 ③
∴x=3y代入②,得
4y+z=7 ④
∴③+④得 x+y+z=7