<s>[INST] 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 
 [/INST] HINT
$$y+x^2= x+y^2\iff y-x-y^2+x^2=0\implies y-x-(y-x)(y+x)=0\implies (y-x)(1-x-y)=0$$
thus
$$y-x=0 \implies y=x \implies x^2+x-2=0$$
or
$$x+y=1\implies x^2-x-1=0$$
</s>