Solve the system by the elimination method.
\[
\begin{array}{r}
3 x-5 y=1 \\
6 x+20 y=8
\end{array}
\]

Step 1 ：Given the system of equations: \[\begin{array}{r} 3x-5y=1 \\ 6x+20y=8 \end{array}\]

Step 2 ：First, we multiply the first equation by 2 to get \(6x - 10y = 2\)

Step 3 ：Then, we subtract the second equation from the result to eliminate y: \((6x - 10y) - (6x + 20y) = 2 - 8\), which simplifies to \(-30y = -6\)

Step 4 ：Solving for y, we get \(y = \frac{-6}{-30} = \frac{1}{5}\)

Step 5 ：Substituting \(y = \frac{1}{5}\) into the first equation, we get \(3x - 5(\frac{1}{5}) = 1\), which simplifies to \(3x - 1 = 1\)

Step 6 ：Solving for x, we get \(x = \frac{2}{3}\)

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{x = \frac{2}{3}, y = \frac{1}{5}}\)