Solve the system by elimination. First, clear the denominators.
\[
\begin{array}{r}
\frac{7 x-1}{5}+\frac{y+10}{6}=28 \\
\frac{x+2}{4}-\frac{x-y}{5}=3
\end{array}
\]

Step 1 ：Given the system of equations: \[\frac{7 x-1}{5}+\frac{y+10}{6}=28 \] and \[\frac{x+2}{4}-\frac{x-y}{5}=3\]

Step 2 ：First, we clear the denominators by multiplying each term by the denominator of the fraction it is in. This gives us two new equations: \[42x + 5y + 44 = 840\] and \[x + 4y + 10 = 60\]

Step 3 ：We then solve the system of equations using the elimination method. This involves adding or subtracting the equations in order to eliminate one of the variables, making it possible to solve for the other variable.

Step 4 ：Doing this, we find the solution to the system of equations is \(x = 18, y = 8\)

Step 5 ：Final Answer: The solution to the system of equations is \(\boxed{x = 18, y = 8}\)