TITLE: Solving two equations of 2nd degree and 2 variables
QUESTION [5 upvotes]: I spent hours trying to solve this system of equations, they're two equations with two variables, and both are 2nd degree equations, I don't know, both equal zero, so each one equals the other, but I came to a step where I'm stuck.
The system is:
\begin{cases}
x^2+y^2-xy=21\\
x^2-8y^2+2xy = 0
\end{cases}

REPLY [5 votes]: Take second eq as $8\cdot y^2-2\cdot x\cdot y-x^2=0$
Solve for $y$
$y=\frac{x}{2},\frac{-x}{4}$
Put in first equation
You would get
$x=\pm\sqrt{28},\pm4$ and $y=\pm\sqrt{7},\mp1$