Which graph represents this system of inequalities? y ≤ –3x – 2 y ≥ 2x + 1
Unfortunately, I cannot provide a graph as an answer. However, you can graph this system of inequalities by following these steps:
1. Graph the line y = -3x - 2:
- Start by plotting two points on the line. For example, you can choose (0, -2) and (1, -5).
- Draw a straight line passing through these two points.
2. Shade the area below the line y = -3x - 2 since it is "y ≤ -3x - 2". This means all points below the line are solutions to the inequality.
3. Graph the line y = 2x + 1:
- Start by plotting two points on the line. For example, you can choose (0, 1) and (1, 3).
- Draw a straight line passing through these two points.
4. Shade the area above the line y = 2x + 1 since it is "y ≥ 2x + 1". This means all points above the line are solutions to the inequality.
The area where the shaded regions overlap represents the solution to the system of inequalities.