https://file.aiquickdraw.com/mathbot/file/1726203888780d0u6bl7c.jpg

Let's solve this system of linear inequalities step by step and match the solution with the correct graph.

The system of inequalities is:
1. \( y > -\frac{1}{3}x + 2 \)
2. \( y > 2x - 3 \)

### 1. First Inequality: \( y > -\frac{1}{3}x + 2 \)
- This is a linear equation with a slope of \( -\frac{1}{3} \) and a y-intercept at \( 2 \).
- The boundary line would be \( y = -\frac{1}{3}x + 2 \), but since the inequality is \( y > -\frac{1}{3}x + 2 \), we need to shade **above** the line.
- Since it is a strict inequality (\( > \)), the boundary line should be **dashed**.

### 2. Second Inequality: \( y > 2x - 3 \)
- This is another linear equation with a slope of \( 2 \) and a y-intercept at \( -3 \).
- The boundary line would be \( y = 2x - 3 \), but since the inequality is \( y > 2x - 3 \), we need to shade **above** this line as well.
- Similar to the first inequality, since it is a strict inequality (\( > \)), the boundary line should also be **dashed**.

### 3. Intersection of the Regions
- We need to look for the region where both inequalities are satisfied, i.e., where the shaded regions overlap.
- Both boundary lines should be dashed (not solid), and the shaded region should be above both lines.

### Analysis of the Graphs:
- **Graph A**: This graph shows shading above the red line and below the blue line, which is incorrect since both inequalities require shading **above** the lines.
- **Graph B**: This graph shows shading above both lines and both lines are dashed, which satisfies both inequalities.
- **Graph C**: This graph shows shading below the red line, which is incorrect for the second inequality.
- **Graph D**: This graph shows shading below the blue line, which is incorrect for the first inequality.

### Correct Answer:
The correct graph is **B**.

Would you like more details or have any further questions? Here are five related questions to consider:

1. How do you determine if you should shade above or below a line in an inequality?
2. What is the significance of using a dashed vs. solid line in inequality graphs?
3. How do the slopes of the lines affect the region where the inequalities overlap?
4. Can you find the point of intersection for the lines \( y = -\frac{1}{3}x + 2 \) and \( y = 2x - 3 \)?
5. What would change if the inequalities were \( \geq \) instead of \( > \)?

**Tip**: Always check the direction of the inequality sign to determine where to shade and whether the boundary line should be solid or dashed.

Which graph shows the solution to the system of linear inequalities? y > -1/3x + 2 and y > 2x - 3.

Learn how to find the correct graphical representation for a system of linear inequalities. This problem explores inequalities y > -1/3x + 2 and y > 2x - 3, including concepts like shading above or below a line and determining whether to use a dashed or solid line.

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