Final answer:
To find the solution set for the inequalities y≤x-3 and y≥-3x+1, graph both inequalities on the same coordinate plane and identify the overlapping region, which represents the solution set.
Step-by-step explanation:
The student is asking about a system of linear inequalities and how to find the solution set for the inequalities y ≤ x - 3 and y ≥ -3x + 1. To solve this, we first graph each inequality on the same coordinate plane. The inequality y ≤ x - 3 represents all the points below or on the line y = x - 3, which has a slope of 1 and a y-intercept at -3. The inequality y ≥ -3x + 1 represents all the points above or on the line y = -3x + 1, which has a slope of -3 and a y-intercept at 1. The solution to the system of inequalities is the region where these two sets of points overlap on the graph. Be sure to shade this region to indicate the solution set.