A number theory problem by Dragan Marković

\[ \large{\begin{cases} x^2+y^2+z^2=18 \\ xy+yz+zx = 9 \end{cases}} \]

Let \(x,y\) and \(z\) be integers satisfying the system of equations above. Find \( |x| + |y| + |z| \).

Notation: \( | \cdot | \) denotes the absolute value function.

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