Question 9
The system of equations $$
\begin{aligned} &\log_{10}(2000xy) \\ &\quad {}- (\log_{10} x)(\log_{10} y) = 4 \end{aligned}
$$ $$
\log_{10}(2yz) - (\log_{10} y)(\log_{10} z) = 1
$$ $$
\log_{10}(zx) - (\log_{10} z)(\log_{10} x) = 0
$$ has two solutions $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2).$ Find $y_1 + y_2.$
\begin{aligned} &\log_{10}(2000xy) \\ &\quad {}- (\log_{10} x)(\log_{10} y) = 4 \end{aligned}
$$ $$
\log_{10}(2yz) - (\log_{10} y)(\log_{10} z) = 1
$$ $$
\log_{10}(zx) - (\log_{10} z)(\log_{10} x) = 0
$$ has two solutions $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2).$ Find $y_1 + y_2.$