<s>[INST] 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.
 [/INST] I will work with 2nd and 3rd equations to solve for $x$ and $y$.
From (3) we get,
$$y=c-2x$$
Substituting the value in (2) we get,
$$x(x+(c-2x))=b$$
$$\implies x^2-cx+b=0$$
$$x=\dfrac{1}{2}(c+\sqrt{c^2-4b}) \text{ or, }\dfrac{1}{2}(c+\sqrt{c^2-4b})$$
If $x=\dfrac{1}{2}(c+\sqrt{c^2-4b})$,then,
$$y=-\sqrt{c^2-4b}$$
Now,we plug the values of x and y in equation in (1),
We get,
$$-\dfrac{1}{4}(c^2+2c\sqrt{c^2-4b}+c^2-4b)\sqrt{c^2-4b}=a$$
And this is the required equation.
[If you use another value of $x$ then,we will get another equation like it.]
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