Question

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.

1. y > x
2. y = -x + 5

Answer 1

To solve the system of inequalities graphically, graph both equations and shade the region that satisfies both inequalities.

Step-by-step explanation:

To solve the system of inequalities graphically, we need to graph the two equations and shade the region that satisfies both inequalities.

First, graph the line y = -x + 5. Plot two points on this line, such as (0, 5) and (5, 0), and draw a straight line connecting these points.

Next, graph the inequality y > x. Determine if the line y = x is part of the solution set by testing a point on the line, such as (0, 0). Since (0, 0) is not a solution to the inequality, we should draw a dashed line to represent y = x. Shade the region above this dashed line, as it satisfies the inequality y > x.

The solution to the system of inequalities is the overlapping shaded region. Select a point within this region, such as (4, 1), and state its coordinates as part of the solution set.