\[\begin{eqnarray*}\log_{10}(2000xy) - (\log_{10}x)(\log_{10}y) & = & 4 \\ \log_{10}(2yz) - (\log_{10}y)(\log_{10}z) & = & 1 \\ \log_{10}(zx) - (\log_{10}z)(\log_{10}x) & = & 0 \\ \end{eqnarray*}\]

The system of equations above has two solutions \((x_{1},y_{1},z_{1})\) and \((x_{2},y_{2},z_{2})\). Find \(y_{1} + y_{2}\).

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