AIME 2000a Problem 9

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