Quite remarkable

Algebra Level 4

\[ \large{ \begin{cases}xy+x+y=23 \\ yz+y+z=31 \\ zx + z+x=47 \end{cases}} \]

Let \(x,y\) and \(z\) be numbers satisfying the system of equations above, enter your answer as the sum of all possible values of \(x,y\) and \(z\).

This is part of the set My Problems and THRILLER

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