Two Thousand Fourteen

Algebra Level 5

log10(2000xy)(log10x)(log10y)=4log10(2yz)(log10y)(log10z)=1log10(zx)(log10z)(log10x)=0\begin{aligned}\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{aligned}

The system of equations above has two solutions (x1,y1,z1)(x_{1},y_{1},z_{1}) and (x2,y2,z2)(x_{2},y_{2},z_{2}). Find y1+y2y_{1} + y_{2}.

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