The problem requires solving a system of two linear equations by graphing. The given equations are: $y = -2x + 2$ $4y + 8x = 8$

1. Problem Description

The problem requires solving a system of two linear equations by graphing. The given equations are:

$y = -2x + 2$

$4y + 8x = 8$

2. Solution Steps

First, let's analyze the given equations.

Equation 1: $y = -2x + 2$ is already in slope-intercept form ($y = mx + b$), where the slope $m = -2$ and the y-intercept $b = 2$.

Equation 2: $4y + 8x = 8$. Let's convert this equation to slope-intercept form:

$4y = -8x + 8$

$y = \frac{-8x + 8}{4}$

$y = -2x + 2$

Notice that both equations are the same. This means that the two equations represent the same line. Therefore, there are infinitely many solutions since every point on the line is a solution to the system.

3. Final Answer

The system of equations has infinitely many solutions. They represent the same line: $y = -2x + 2$.