To solve the system of equations using substitution, we have the following two equations:
- \(-4x + 6y = 38\)
- \(x - 5y = -20\)
First, let's solve the second equation for \(x\):
\[ x - 5y = -20 \] \[ x = -20 + 5y \]
Now we can substitute this expression for \(x\) into the first equation:
\[ -4(-20 + 5y) + 6y = 38 \]
Distributing \(-4\):
\[ 80 - 20y + 6y = 38 \]
Now, combine like terms (\(-20y + 6y\)):
\[ 80 - 14y = 38 \]
Next, isolate the \(y\) term by subtracting 80 from both sides:
\[ -14y = 38 - 80 \] \[ -14y = -42 \]
Now, divide both sides by \(-14\):
\[ y = \frac{-42}{-14} = 3 \]
Now that we have the value of \(y\), we can substitute it back into the equation for \(x\):
\[ x = -20 + 5y \] \[ x = -20 + 5(3) \] \[ x = -20 + 15 \] \[ x = -5 \]
Therefore, the solution to the system of equations is:
\[ \boxed{(-5, 3)} \]