If $x^2+y^2-xy-x-y+1=0$ ($x,y$ real) then calculate $x+y$ If $x^2+y^2-xy-x-y+1=0$ ($x,y$ real) then calculate $x+y$
Ideas for solution include factorizing the expression into a multiple of $x+y$ and expressing the left hand side as a sum of some perfect square expressions.  

The value of $x+y$ is not determined by the first equation. For $x=0$ we obtain $y^2-y+1=0$, so that $x+y=\frac{\pm \sqrt{-3}+1}{2}$. This is certainly not equal to $2$.
