Not Three Egyptian Fractions

Algebra Level 2

\[ \begin{eqnarray} \frac{1}{x} + \frac{1}{y} &=& \frac{1}{3}\\ \frac{1}{x} + \frac{1}{z} &=& \frac{1}{5}\\ \frac{1}{y} + \frac{1}{z} &=& \frac{1}{7} \\ \end{eqnarray} \]

Given the system of equations above, what is the value of \( \frac{z}{y}\)?

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