Solve the system of equations ... Solve the system of equations : 
(EDIT : The problem does not say anything about the nature of $x$ and $y$ (integer, natural number ,..etc.) )
$4xy + 4(x^2 + y^2) + {\frac {3} { (x+y) ^ 2 } } = \frac {85} {3} $
$2x + {\frac {1} {x+y}} = \frac {13} {3}$
I do not know how to approach these types of problems. I tried finding value of $\frac {1} {x+y}$ in terms of $x$ and $y$, but it complicates the problem even more.
Can anyone provide a pointer to what should be done ?

Perhaps this can help: Let $x+y=v$ and $x-y=w$, then the equations can be written as 
\begin{align*}
3\left(v^2+\frac{1}{v^2}\right)+w^2 & = \frac{85}{3}\\
\left(v+\frac{1}{v}\right)+w & = \frac{13}{3}.
\end{align*}
Now let $v+\frac{1}{v}=t$, then the system can be rewritten as
\begin{align*}
3t^2+w^2 & = \frac{85}{3}+6\\
t+w & = \frac{13}{3}.
\end{align*}
Now solve for $t$ and $w$...
