To solve the system of equations:
- \(-4x + 6y = 38\)
- \(x - 5y = -20\)
We can use the substitution or elimination method. Let's use the substitution method.
From the second equation, solve for \(x\):
\[ x = 5y - 20 \]
Now substitute \(x\) into the first equation:
\[ -4(5y - 20) + 6y = 38 \]
Distributing gives:
\[ -20y + 80 + 6y = 38 \]
Combining like terms:
\[ -14y + 80 = 38 \]
Subtract 80 from both sides:
\[ -14y = 38 - 80 \] \[ -14y = -42 \]
Divide by -14:
\[ y = \frac{-42}{-14} = 3 \]
Now substitute \(y\) back into the equation for \(x\):
\[ x = 5(3) - 20 \] \[ x = 15 - 20 \] \[ x = -5 \]
So, the solution to the system of equations is:
\[ (x, y) = (-5, 3) \]
Therefore, the answer is \((−5, 3)\).