To solve the system of equations using substitution, we will start with the two equations given:
- \(-4x + 4y = -40\)
- \(y = 3x - 4\)
We can substitute the expression for \(y\) from the second equation into the first equation.
Substituting \(y\) in the first equation:
\[ -4x + 4(3x - 4) = -40 \]
Now, distribute the 4:
\[ -4x + 12x - 16 = -40 \]
Combine like terms:
\[ (12x - 4x) - 16 = -40 \]
\[ 8x - 16 = -40 \]
Now, add 16 to both sides:
\[ 8x = -40 + 16 \]
\[ 8x = -24 \]
Next, divide both sides by 8:
\[ x = -3 \]
Now that we have \(x\), we substitute it back into the second equation to find \(y\):
\[ y = 3(-3) - 4 \]
\[ y = -9 - 4 \]
\[ y = -13 \]
The solution to the system of equations is:
\[ (x, y) = (-3, -13) \]