An algebra problem by Yan Yau Cheng

Algebra Level 3

Let \(x\), \(y\), and \(z\) be reals satisfying the following:

\[z = 2x + 4y + 5\] \[-x^2 + xy + y^2 = 2z^2+8\] \[5x^2 + 3xy = -8-z^2\]

If \(y = -\frac ab\) for positive co-prime integers \(a\) and \(b\), find \(a+b\)

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