To solve the system of equations, we have:
- \( 2x + 4y = 12 \)
- \( y = \frac{1}{4}x - 3 \)
We can solve this system using substitution. We'll substitute \( y \) from the second equation into the first equation.
Substituting \( y \) into the first equation:
\[ 2x + 4\left( \frac{1}{4}x - 3 \right) = 12 \]
Now, simplify the equation:
\[ 2x + 4 \cdot \frac{1}{4}x - 4 \cdot 3 = 12 \]
This simplifies to:
\[ 2x + x - 12 = 12 \]
Combine like terms:
\[ 3x - 12 = 12 \]
Add 12 to both sides:
\[ 3x = 24 \]
Divide by 3:
\[ x = 8 \]
Now that we have \( x \), we can substitute it back into the second equation to find \( y \):
\[ y = \frac{1}{4}(8) - 3 \]
This simplifies to:
\[ y = 2 - 3 = -1 \]
Thus, the solution to the system of equations is \( (8, -1) \).
Therefore, the correct answer is:
(8, –1)