To solve this system of equations by graphing, we will first look at the two given equations and then plot them on the graph.

The two equations are:

1. $y = 4x + 5$
2. $y = -4x + 5$

Steps for graphing:

1. Equation 1: $y = 4x + 5$

   • This is in slope-intercept form ($y = mx + b$), where:
     • Slope (m) = 4
     • Y-intercept (b) = 5
   • The graph will start at the point (0, 5) on the y-axis and increase by 4 units for every 1 unit moved to the right along the x-axis.

2. Equation 2: $y = -4x + 5$

   • Similarly, for this equation:
     • Slope (m) = -4
     • Y-intercept (b) = 5
   • The graph will also start at (0, 5) on the y-axis, but will decrease by 4 units for every 1 unit moved to the right along the x-axis.

Graphing the system:

• Plot both lines on the graph, marking the points and drawing the lines through them.
• Since both equations have the same y-intercept of 5, they will intersect at the point (0, 5).
• The lines will have slopes of 4 and -4, which means they will be moving in opposite directions.

Interpretation of the graph:

The point of intersection (0, 5) is the solution to the system of equations.

Thus, the solution to the system of equations is: $\boxed{(0, 5)}$

Would you like further details on graphing these lines or any other assistance? Here are some follow-up questions:

1. How would the solution change if the y-intercepts were different for both lines?
2. What happens when the slopes of the two equations are equal?
3. How do you determine the slope from the equation of a line?
4. What does the slope represent in real-world scenarios?
5. How can the graphing method be used to solve systems of three equations?

Tip: To graph a line quickly, start by plotting the y-intercept and then use the slope to find another point on the line.