Answer:
I can provide you with a step-by-step explanation of how to graph the given system of inequalities on the provided coordinate plane.
To graph y > 2x + 4:
1. Rearrange the inequality to get y - 2x - 4 > 0.
2. Identify two points that satisfy the inequality, such as (0, 4) and (2, 0).
3. Plot these points on the coordinate plane.
4. Draw a straight line passing through these two points.
5. Shade the region above the line, as the inequality is a strict greater than (>).
To graph x + y ≤ 6:
1. Rearrange the inequality to get y ≤ 6 - x.
2. Identify two points that satisfy the inequality, such as (0, 6) and (6, 0).
3. Plot these points on the coordinate plane.
4. Draw a straight line passing through these two points.
5. Shade the region below the line and including the line itself, as the inequality is a less than or equal to (≤).
The solution to the system of inequalities is the region that satisfies both inequalities simultaneously, which is the overlapping shaded area.
Please let me know if you need any further assistance or clarification in graphing the solution on the provided coordinate plane.
