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
答
x-3y+z=0, (1)
3x+3y-4z=0 (2)
(1)+(2)得:
4x-3z=0
x=3z/4
代入(1)得:
y=7z/12
所以:x:y:z=3/4:7/12:1
同乘以12得:
x:y:z=9:7:12
答
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
则
x:y:z
=(3/4)z:(7/12)z:z
=9:7:12