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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