# Is $$x=y=z=0$$?

Algebra Level 5

$\large{\begin{cases} (x-2)(y-2)=4 \\ (y-3)(z-3)=9 \\ (z-4)(x-4)=16 \end{cases}}$

Let $$x,y$$ and $$z$$ be positive rational numbers satisfying the system of equations above, find the value of $$5x+7y-z$$.

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