To solve the system of equations:
- \( -4x + 6y = 38 \)
- \( x - 5y = -20 \)
We can solve it using the substitution or elimination method. Let's use the substitution method for simplicity.
First, we'll solve the second equation for \( x \):
\[ x = 5y - 20 \]
Now we will substitute this expression for \( x \) in the first equation:
\[ -4(5y - 20) + 6y = 38 \]
Expanding this gives:
\[ -20y + 80 + 6y = 38 \]
Combining like terms:
\[ -20y + 6y + 80 = 38 \] \[ -14y + 80 = 38 \]
Now, subtract 80 from both sides:
\[ -14y = 38 - 80 \] \[ -14y = -42 \]
Dividing both sides by -14:
\[ y = 3 \]
Now that we have \( y \), we'll substitute it back into the equation for \( x \):
\[ x = 5(3) - 20 \] \[ x = 15 - 20 \] \[ x = -5 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-5, 3) \]
The correct response is:
\((−5, 3)\)