Question

Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations. y=x+3 𝑦 = 𝑥 + 3 −4x+4y=28 − 4 𝑥 + 4 𝑦 = 28 (2 points)

Answer 1

To solve the given system of linear equations, we will first rewrite the equations:

1. The first equation is already in slope-intercept form: \[ y = x + 3 \]

2. For the second equation \( -4x + 4y = 28 \), we need to rearrange it into slope-intercept form (y = mx + b): \[ 4y = 4x + 28 \] \[ y = x + 7 \]

Now we have two equations to graph:

1. \( y = x + 3 \)
2. \( y = x + 7 \)

Graph Description

When you graph these two lines on a coordinate plane:

• The line represented by \( y = x + 3 \) will have a slope of 1 and a y-intercept at \( (0, 3) \). The line will rise from left to right, passing through points like \( (-1, 2) \) and \( (1, 4) \).

• The line represented by \( y = x + 7 \) also has a slope of 1 but a higher y-intercept at \( (0, 7) \). This line will also rise from left to right, passing through points like \( (-1, 6) \) and \( (1, 8) \).

Visual Characteristics

• Parallel Lines: Upon graphing, you will observe that both lines have the same slope (1) but different y-intercepts. The first line hits the y-axis at (0, 3), while the second hits at (0, 7).

Conclusion About the Solution

Since the two lines are parallel and will never intersect, this tells us that the system of linear equations has no solution. In other words, the equations represent two lines that do not share any points in common on the graph. Therefore, the system is considered inconsistent.