若4x-3y-6z=0,x+2y-7z=0(xyz≠0),则x:y:z=_.

问题描述:

若4x-3y-6z=0,x+2y-7z=0(xyz≠0),则x:y:z=______.

x+2y-7z=0可化为x=7z-2y,
把x=7z-2y代入4x-3y-6z=0中,
得28z-8y-3y-6z=0,
22z-11y=0,
y=2z,
把y=2z代入4x-3y-6z=0中,
则x=7z-4z,
x=3z,
所以x:y:z=3z:2z:z=3:2:1.