答：缺少了y^2吧?
x^2+y^2-2xy+6x-6y+9=0
(x-y)^2+6(x-y)+9=0
(x-y+3)^2=0
x-y+3=0
x-y=-3少了2y^2x^2-2xy+2y^2+6x-6y+9=0
x^2-2xy+y^2+y^2+6x-6y+9=0
(x-y)^2+6(x-y)+9+y^2=0
(x-y+3)^2+y^2=0
所以：

x-y+3=0
y=0
解得：
x=-3，y=0