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?

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.