已知5X-4Y-7Y=0,4X-3Y-6Z=0,则X:Y:Z=?

问题描述:

已知5X-4Y-7Y=0,4X-3Y-6Z=0,则X:Y:Z=?

5X-4Y-7Y=0 15X-12Y-21Z=0 (1)
4X-3Y-6Z=0 16X-12Y-24Z=0 (2)
(2)-(1),消去Y,可得 X-3Z=0 X=3Z 带入(1)
15×3Z-12Y-21Z=0 ,解得 24Z=12Y
Y=2Z
所以X:Y:Z=3Z:2Z:Z=3:2:1