已知方程组x-3y+z=0,3x+3y-4z=0有解,求x:y:z

问题描述:

已知方程组x-3y+z=0,3x+3y-4z=0有解,求x:y:z

x-3y+z=0.(1)
3x+3y-4z=0.(2)
(1)+(2)得
4x-3z=0
4x=3z
x=(3/4)z
代入(1)得
(3/4)z-3y+z=0
3y=(7/4)z
y=(7/12)z

x:y:z
=(3/4)z:(7/12)z:z
=9:7:12