Simple System of Equations Part 3

Algebra Level 4

xyz+3x+3yz=106xyz+3z+3xy=79xyz+3y+3xz=82(x+1)(y+1)(z+1)= ?\begin{aligned}xyz + 3x + 3yz&=&106 \\ xyz + 3z + 3xy&=&79 \\ xyz+ 3y + 3xz&=&82 \\ (x+1)(y+1)(z+1) &=& \ ? \end{aligned}

See Part 1 and Part 2.

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