I read this problem on a site:

$\displaystyle x^2-xy+y^2=21$

$\displaystyle x^2+xy-8y^2=0$

I believe it's not possible to isolate either x or y in either equation using standard methods, right? It was suggested to actually use the quadratic formula to solve in terms of a single variable. I also read that the second equation can be factored, but I can't seem to figure out how the factoring was done. Apparently it factors into:

(x+4y)(x–2y)