Just elegancy required 2

Algebra Level 4

\[\begin{cases} xy+x+y=23 \\ xz+x+z=41 \\ yz+y+z=27 \end{cases}\]

Let the two solution set of \(x,y,z\) be \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\), find \(x_1 y_1 z_1 + x_2 y_2 z_2\).

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