已知4X-3Y-6Z=0,X+2Y-7Z=0,(XY不等于0）,求代数式5X^2+1Y^2-Z^2/2X^2-3Y^2-10Z^2的值

已知4X-3Y-6Z=0,X+2Y-7Z=0,(XY不等于0）,求代数式5X^2+1Y^2-Z^2/2X^2-3Y^2-10Z^2的值
已知4X-3Y-6Z=0,X+2Y-7Z=0,(XY不等于0）,求代数式5X^2+1Y^2-Z^2/2X^2-3Y^2-10Z^2的值

已知4X-3Y-6Z=0,X+2Y-7Z=0,(XY不等于0）,求代数式5X^2+1Y^2-Z^2/2X^2-3Y^2-10Z^2的值
4X-3Y-6Z=0 (1)
X+2Y-7Z=0 (2)
(2)*4-(1)
4X+8Y-28Z-4X+3Y+6Z=0
11Y-22Z=0
Y=2Z
(1)*2+(2)*3
8X-6Y-12Z+3X+6Y-21Z=0
11X-33Z=0
X=3Z
代入(5X^2+1Y^2-Z^2)/(2X^2-3Y^2-10Z^2)
=(45Z^2+4Z^2-Z^2)/(18Z^2-32Z^2-10Z^2)
=48Z^2/(-24Z^2)
=-2

x=3z y=2z
原式=-12

-2

4X-3Y-6Z=0
X+2Y-7Z=0 解之得 x=3z y=2z
把x=3z y=2z 带入代数式的原式=-12

-12