解方程组x^2-2xy-3y^2=0,x-2y=6

题目

解方程组x^2-2xy-3y^2=0,x-2y=6

答案

x^2-2xy-3y^2
=(x+y)(x-3y)
=(x-2y+3y)(x-2y-y)
=(6+3y)(6-y)=0
则,6+3y=0或6-y=0
得y1=-2或y2=6
x1=2 ,x2=18
方程组的解为 x1=2 ,y1=-2或x2=18,y2=6