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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