# A System of Nonlinear Equations

Algebra Level 2

Given the system of equations $\begin{cases} x(x+y) &=& 9 \\ y(x+y) &=& 16 \end{cases}$ the value of $$xy$$ can be written as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are positive coprime integers. Find $$a+b$$.

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