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)

1 answer

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)