To solve the system of equations:
- \(-4x + 6y = 38\)
- \(x - 5y = -20\)
We can solve these equations using the substitution or elimination methods. Let's use the substitution method.
First, solve the second equation for \(x\):
\[ x = 5y - 20 \]
Now we can substitute this expression for \(x\) in the first equation:
\[ -4(5y - 20) + 6y = 38 \]
Expanding this:
\[ -20y + 80 + 6y = 38 \]
Combine like terms:
\[ -14y + 80 = 38 \]
Now, isolate \(y\) by subtracting 80 from both sides:
\[ -14y = 38 - 80 \] \[ -14y = -42 \]
Now, divide by -14:
\[ y = \frac{-42}{-14} = 3 \]
Now that we have \(y\), substitute back to find \(x\) using the expression \(x = 5y - 20\):
\[ x = 5(3) - 20 \] \[ x = 15 - 20 \] \[ x = -5 \]
Thus, the solution to the system of equations is:
\[ x = -5, \quad y = 3 \]
The solution can be written as the ordered pair \((-5, 3)\).