A system within a system

Algebra Level 4

\[\large \frac{1}{xy} + \frac{2}{yz} + \frac {3}{xz} = \frac {29}{72} \\ \large \frac{4}{xy} + \frac{5}{yz} + \frac {6}{xz} = \frac {17}{18} \\ \large \frac{7}{xy} - \frac{8}{yz} + \frac {9}{xz} = \frac {43}{72} \]

Given the system of equations above.

Find

\[\large (x+y+z)^{2}. \]

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