Final answer:
To represent the solution to the system of inequalities 3x - 5y < 15 and y > -x + 1, graph the inequalities on a coordinate plane, shade the regions, and find the overlap.
Step-by-step explanation:
To represent the solution to the system of inequalities 3x - 5y < 15 and y > -x + 1, we need to graph the inequalities on a coordinate plane and shade the region that satisfies both inequalities.
First, let's graph the inequality 3x - 5y < 15. To do this, we can draw the line 3x - 5y = 15 as a dashed line, since the inequality sign is <. Then, we shade the region below this line, as this represents the values that satisfy 3x - 5y < 15.
Next, let's graph the inequality y > -x + 1. We can draw the line y = -x + 1 as a solid line, since the inequality sign is >. Then, we shade the region above this line, as this represents the values that satisfy y > -x + 1.
The solution to the system of inequalities is the region where both shaded regions overlap.