Large numbers, easy trick

Algebra Level 3

\[\begin{cases} 5732x + 2134y + 2134z = 7866 \\ 2134x + 5732y + 2134z = 670 \\ 2134x + 2134y + 5732z = 11464 \end{cases} \]

Let \(x,y\) and \(z\) be real numbers satisfying the system of equations above. Find \(xyz\).

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