Solve the system of inequalities by graphing.
y < 3x + 5
3x - y <= 4
Coordinates
To graph the system of inequalities, we will start by graphing each inequality separately and then determining the overlapping region.
1. Graphing y < 3x + 5:
- First, graph the line y = 3x + 5. To do so, plot two points on the line. We can choose x = 0, which gives us y = 5 (point A), and x = -1, which gives us y = 2 (point B).
- Draw a dotted line through points A and B to represent y = 3x + 5.
- Since y < 3x + 5, we need to shade the region below the dotted line. This indicates that any point below the line satisfies the inequality.
2. Graphing 3x - y <= 4:
- Rearrange the inequality to y >= 3x - 4 to make it easier to graph.
- Graph the line y = 3x - 4. Plot two points on the line using x = 0, which gives us y = -4 (point C), and x = 1, which gives us y = -1 (point D).
- Draw a solid line through points C and D to represent y = 3x - 4.
- Since y >= 3x - 4, we need to shade the region above the solid line. This indicates that any point above the line satisfies the inequality.
The overlapping region of the shaded areas represents the solution to the system of inequalities. Here's a rough sketch of the graph:
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The overlapping region should be below the dotted line (y < 3x + 5) and above the solid line (y >= 3x - 4).