Question

Which system of linear inequalities is represented by the graph?

y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x + 1

Answer 1

To determine which system of linear inequalities is represented by the graph, you need to examine the lines and the shaded regions in the graph.

1. **Identify the lines** from the inequalities:
- **From y > x - 2**: This line, \( y = x - 2 \), should be dashed because it is a "greater than" inequality, indicating that points on the line are not included in the solution.
- **From y < x + 1**: This line, \( y = x + 1 \), should also be dashed for the same reason.

2. **Determine the shaded regions**:
- For \( y > x - 2 \): The region above the line \( y = x - 2 \) will be shaded.
- For \( y < x + 1 \): The region below the line \( y = x + 1 \) will be shaded.

3. **Combine the two conditions**:
- The solution to the system will be the overlapping region that satisfies **both** inequalities.

If the graph shows a region above the line \( y = x - 2 \) and below the line \( y = x + 1 \), then it matches the first option:

**y > x - 2 and y < x + 1**.

Based on the descriptions of each option, the correct answer is:

**y > x - 2 and y < x + 1**.