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To determine which system of inequalities matches the graph, we need to analyze the shaded regions and the boundary lines. Here’s how we break it down:

### 1. Identify the boundary lines:
- There are two boundary lines shown: one is **solid** and one is **dashed**. The solid line indicates that the inequality is either ≤ or ≥, and the dashed line indicates strict inequality (< or >).
- By examining the slopes and y-intercepts, we can write the equations of the lines:
   - The **solid line** has a positive slope and intercepts the y-axis at \(y = -6\), and it goes up by 1 for every increase of 1 in \(x\). This suggests the equation \( y \geq x - 6 \).
   - The **dashed line** has a negative slope and intercepts the y-axis at \(y = 9\), and it falls by 5 units for every increase of 1 in \(x\). This suggests the equation \( y \leq -5x + 9 \).

### 2. Identify the shading:
- The area **above** the dashed line is shaded, implying \( y \geq x - 6 \).
- The area **below** the solid line is shaded, implying \( y \leq -5x + 9 \).

### 3. Match the inequalities:
- From this analysis, the system of inequalities is:
   \[
   y \leq -5x + 9 \quad \text{AND} \quad y \geq x - 6
   \]

This matches **option B**: \( y \leq -5x + 9 \quad \text{AND} \quad y \geq 6x - 10 \).

### Final Answer: **B**

Would you like more details on how to solve inequalities graphically or have any questions?

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Here are 5 related questions to expand on this topic:
1. How do you graph inequalities with two variables?
2. What is the difference between strict inequalities and inclusive inequalities in graphs?
3. How can you solve a system of inequalities using substitution or elimination?
4. How do boundary lines affect the solution region in an inequality system?
5. Can a system of inequalities have more than one solution region?

**Tip:** Always double-check the slope and intercept when matching inequalities to graphs.

Which of the following systems of inequalities matches the graph shown?

Determine which system of inequalities matches the given graph, analyzing slope, intercept, and shaded regions. This problem covers graphing inequalities and identifying the correct solution from a set of options. Suitable for students in Grades 8-10.

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