The graph shows two lines representing the equations y = 2x + 5 and x + y = 1.
Which ordered pair is in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1?
The solution to this system of inequalities is where the shaded regions of both inequalities overlap.
The first inequality, y ≥ 2x + 5, is represented by the line y = 2x + 5. The shaded region is above this line.
The second inequality, x + y ≤ 1, is represented by the line x + y = 1. The shaded region is below this line.
The overlap between the two shaded regions is the area where both inequalities are satisfied.
Looking at the graph, the region where both inequalities overlap is in the bottom left quadrant bounded by the x-axis, y-axis, and line x + y = 1.
One ordered pair in this region is (0,1). Hence, (0,1) is in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1.