How to solve these equations for x and y.. equations are 

$(x-y)(x+2y)(2x+y) = 20$ 

and

$x^2+xy+y^2 = 7$

i want the METHOD not the solutions 

1073177
Use Sylvester's dialytic eliminant:
$\begin{vmatrix}
-2&-7x&3x^2&2x^3-20&0\\
0&-2&-7x&3x^2&2x^3-20\\
1&x&x^2-7&0&0\\
0&1&x&x^2-7&0\\
0&0&1&x&x^2-7\\
\end{vmatrix}$
$(=79x^6-1022x^4-80x^3+2891x^2+1120x-972)$
to get rid of the $y$s. Equate it to $0$, solve it for $x$, then substitute each value into one of the original equations (preferably the simpler one), then solve for the corresponding $y$.
