Solve the system of equations.

Question

2x+8y=8

2x−4y=−16
(1 point)
(
,
)

Answer 1

To solve the system of equations:

1. \( 2x + 8y = 8 \) \quad (Equation 1)
2. \( 2x - 4y = -16 \) \quad (Equation 2)

We can use the substitution or elimination method. Let's use the elimination method.

First, let's simplify both equations.

Step 1: Simplify Equation 1

Divide the entire equation by 2:

\[ x + 4y = 4 \quad (Equation 1') \]

Step 2: Simplify Equation 2

Divide the entire equation by 2:

\[ x - 2y = -8 \quad (Equation 2') \]

Now we have:

1. \( x + 4y = 4 \) \quad (1')
2. \( x - 2y = -8 \) \quad (2')

Step 3: Eliminate \( x \)

Subtract Equation (2') from Equation (1'):

\[ (x + 4y) - (x - 2y) = 4 - (-8) \]

This simplifies to:

\[ 6y = 12 \]

Step 4: Solve for \( y \)

Divide both sides by 6:

\[ y = 2 \]

Step 5: Solve for \( x \)

Substitute \( y = 2 \) back into Equation (1'):

\[ x + 4(2) = 4 \]

\[ x + 8 = 4 \]

Subtract 8 from both sides:

\[ x = 4 - 8 \]

\[ x = -4 \]

Final Solution:

The solution to the system of equations is:

\[ (x, y) = (-4, 2) \]

So the answer is:

\[ \boxed{(-4, 2)} \]