# Complex System of Equations

Algebra Level 5

For how many ordered pairs $$(a,b)$$ of complex numbers does the system of equations $\begin{cases} x^2y-x=a\\ xy^2+y=b \end{cases}$ have exactly one complex number solution?

Details and assumptions

A complex number solution is an ordered pair of complex numbers $$(x,y)$$ that satisfies both equations.

Clarification: $$a, b, x$$ and $$y$$ are all complex numbers. As an explicit example, $$(x,y) = (i, i)$$ is a solution to $$(a,b) = (-2i, 0 )$$.

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