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I want to solve the following two equations in two unknowns:

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The unknowns are $x$ and $y$. Please help me.

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Is this a homework? Also, what have you tried and what kind of help (e.g. full solution) do you expect? Be more specific.. – Marek Jan 19 '13 at 11:00
@Marek Excuse me, Something does not seem to mind. – aliakbar Jan 19 '13 at 11:02

The second equation can be solved for $y$: $$y=x/(1+(b/x))=x^2/(x+b)\tag1$$ Now rewrite the first equation as $$-2a-bcy^2+2cx^2(x-y)=0$$ and use (1) to get an equation involving only $x$. Come back when you've done that, and we'll see what we can do from there.

EDIT: Maple says $x=\alpha$, $y=\alpha^2/(b+\alpha)$, where $\alpha$ is a root of $$bcz^4+2b^2cz^3-2az^2-4abz-2ab^2=0$$

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