The system of equations provided is:

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

To solve this system by graphing, let's break down the steps:

Step 1: Graph the first equation $y = -4x + 1$

This is in slope-intercept form $y = mx + b$, where:

• The slope $m = -4$, meaning the line will go down 4 units for every 1 unit you move to the right.
• The y-intercept $b = 1$, which is where the line crosses the y-axis.

Step 2: Graph the second equation $2x - y = 5$

Rearrange it to the slope-intercept form: $y = 2x - 5$ Now, we see that:

• The slope $m = 2$, meaning the line goes up 2 units for every 1 unit to the right.
• The y-intercept $b = -5$, which is where the line crosses the y-axis.

Step 3: Plot the lines on a graph

• For $y = -4x + 1$, start at the point $(0, 1)$ and use the slope of -4 to plot another point. Draw the line through these points.
• For $y = 2x - 5$, start at the point $(0, -5)$ and use the slope of 2 to plot another point. Draw the line through these points.

Step 4: Find the intersection

The solution to the system is where the two lines intersect.

Would you like me to generate a graph to show the solution visually?