How do I eliminate $x$ and $y$ from the system $x^2 y= a$, $x(x+y)= b$, $2x+y=c$ to get a single equation in $a$, $b$, $c$? Alright, a homework problem.
I'm stuck at this question, 

Eliminate $x$ and $y$ from the given equations to get a single
  equation in terms of $a$ , $b$ and $c$
$$\begin{align}
x^2 y &= a \\
x(x+y) &= b \\
2x+y &=c
\end{align}$$

Let me tell you what I tried, I tried to get $y$ from one equation and substitute in the other two. Turns out that I'm not able to fully get rid of both $x$ and $y$. Help please.

Combine the first and second equations to eliminate $y$:
$x(x+\frac{a}{x^2})=b$
which tidies to
$x^2+\frac{a}{x}=b$ ....... (1)
combine the second and third equations to eliminate $y$:
$x(x+c-2x)=b$
which tidies to
$x^2-cx+b=0$
solving this quadratic gives
$x=\frac{c \pm \sqrt{c^2-4b}}{2}$
which you can substitute into equation (1):
$\left(\frac{c \pm \sqrt{c^2-4b}}{2}\right)^2+\frac{a}{\left(\frac{c \pm \sqrt{c^2-4b}}{2}\right)}=b$
