The problem asks us to solve the system of equations $y = -2x + 2$ $4y + 8x = 8$ by graphing.

1. Problem Description

The problem asks us to solve the system of equations

$y = -2x + 2$

$4y + 8x = 8$

by graphing.

2. Solution Steps

First, let's simplify the second equation:

$4y + 8x = 8$

Divide by 4:

$y + 2x = 2$

Subtract $2x$ from both sides:

$y = -2x + 2$

Now we have the two equations:

$y = -2x + 2$

$y = -2x + 2$

Since both equations are identical, they represent the same line. This means that there are infinitely many solutions, and any point on the line $y = -2x + 2$ is a solution to the system of equations.

To graph the line, we can find two points on the line.

If $x=0$, then $y = -2(0) + 2 = 2$. So the point $(0, 2)$ is on the line.

If $x=1$, then $y = -2(1) + 2 = 0$. So the point $(1, 0)$ is on the line.

Since the two equations are the same line, the solution is all points on the line $y = -2x + 2$.

3. Final Answer

Infinitely many solutions. The two equations represent the same line.