Question

2x + 4y = 12
y = A system of equations. 2 x plus 4 y equals 12. y equals StartFraction one-fourth EndFraction x minus 3.x – 3
What is the solution to the system of equations?

(–1, 8)
(8, –1)
(5, StartFraction one-half EndFraction)
(StartFraction one-half EndFraction, 5)

Answer 1

To solve the system of equations, we have:

1. \( 2x + 4y = 12 \)
2. \( y = \frac{1}{4}x - 3 \)

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)**