System of equations $x + xy + y = 11$ and $yx^2 + xy^2 = 30$ I have problem with solving this one.
Total number of solutions from system of equations?
\begin{cases} 
x + xy + y = 11 \\ 
x^2y + y^2x = 30 
\end{cases}
There is a system of equation and I have tried to get some normal solutions, but I always get the fourth degree polynomial from which I do not know how to get simple 'x's and 'y's. I know that task asks me to just find total number, but I would like to know which solutions are those. This is adjusted for high school mathematics level. 

There are exactly $4$ solutions (over characteristic zero), namely $(x,y)=(1,5),(2,3),(3,2),(5,1)$. To see this, note first that $y+1\neq 0$. In fact, for $y=-1$ the first equations implies $11=0$, a contradiction. It follows that $x=-\frac{y-11}{y+1}$. Substituting this into the second equation gives
$$
(y - 1)(y - 2)(y - 3)(y - 5)=0.
$$
