RMO 1994

The integer solutions for \(x\) & \(y\) in the equations

\(5x (1+\frac{1}{x^2+y^2}) = 12\) & \(5y (1-\frac{1}{x^2+y^2}) = 4\),

are \(a\) & \(b\). Find \(a + b\).

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