How to find result of system $x+y^2-4=0$ and $y+x^2-4=0$ without using the quartic formula How do I get the values of $x$ and $y$, without using the quartic formula?
\begin{align*}
\begin{cases} x+y^2-4=0 \\ y+x^2-4=0  \end{cases}
\end{align*}

Subtract the first equation from the second to obtain:
$$x^2-y^2+y-x=0\Leftrightarrow \\
(x-y)(x+y-1)=0 $$
