2. Given real numbers $x, y$ satisfy
$$
\begin{array}{l}
\sqrt{125 x-16}+\sqrt{25-8 y}=6, \\
\sqrt{25-80 x}+\sqrt{12.5 y-16}=6 .
\end{array}
$$

Then $\frac{x}{y}=$
2.0.1.

Subtracting the two equations yields
$$
\begin{array}{l}
\sqrt{125 x-16}-\sqrt{12.5 y-16}+ \\
(\sqrt{25-8 y}-\sqrt{25-80 x})=0 \\
\Rightarrow(x-0.1 y)\left(\frac{125}{\sqrt{125 x-16}+\sqrt{12.5 y-16}}+\right. \\
\left.\frac{80}{\sqrt{25-80 x}+\sqrt{25-8 y}}\right)=0 \\
\Rightarrow x-0.1 y=0 \Rightarrow \frac{x}{y}=0.1 .
\end{array}
$$