Find all ordered pairs such that $x + y^2 = 2$ and $y + x^2 = 2$ How can I find all ordered pairs $(x,y)$ such that $x + y^2 = 2$ and     $y + x^2 = 2$?
A solution/explanation would be greatly appreciated.
If it helps, the solutions given in the textbook are 
x=-2, y=-2; x=1, y=1; x= (1+root 5)/2, y=(1-root 5)/2;            x= (1-root 5)/2, y=(1+root 5)/2 

Well $x+y^2=y+x^2$ so $x-y=x^2-y^2=(x-y)(x+y) $
If $x-y=0$ then $x=y$ and $x+x^2=2$.  We can use the the quadratic equation to solve that.
If $x-y\ne 0$ then $1=(x+y) $ and $y=1-x $
So $x+y^2=x^2+y=x^2-x+1=2$ and we can use the quadratic equation to solve that.
