Excel in math, science, and engineering

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\[ \begin{eqnarray} xy+z&=&26 \\ xz+y&=& 29 \\ yz+x&=&34 \end{eqnarray} \]

If \(x,y,z\) are integers satisfying the system of equations above, what is the value of \(x+y+z\)?

See Part 1 and Part 3.

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