# There's A Maximum?

Number Theory Level 5

$\begin{cases} xy+yz+xz+2(x+y+z)=53 \\ x(yz-1)=y+z-2 \end{cases}$

Given that $$x,y$$ and $$z$$ are positive integers satisfying the system of equations above, find the maximum value of $$x+y$$.

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