Final answer:
The solution to the system of inequalities y ≤ ⅓x - 4 and y > -7 is found by graphing each inequality and then looking for the overlapping shaded region, which represents all the points that satisfy both inequalities.
Step-by-step explanation:
The question involves determining the solution set for a system of inequalities and possibly graphing it. The given inequalities state that y ≤ ⅓x - 4 and y > -7. To solve this system, one would graph both inequalities on the same coordinate plane:
- For the inequality y ≤ ⅓x - 4, one would graph the line y = ⅓x - 4 and shade the area below it since the inequality is 'less than or equal to'.
- For the inequality y > -7, one would draw a horizontal dashed line at y = -7 and shade the area above it because the inequality is 'greater than'.
The solution set consists of the region where both shadings overlap. It's important to note that this region will not include the line y = -7 since the inequality is strict ('greater than' and not 'greater than or equal to').