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To determine which system of linear inequalities is best represented by the shaded region in the graph, we should examine the lines, their equations, and the shaded region's location in relation to these lines.

1. **Identify the equations of the lines**: 

   - The first line intersects the y-axis at \( y = -9 \) and has a positive slope, appearing to rise by 3 for every 1 unit it moves to the right (slope of 3). This suggests the equation:
     \[
     y = 3x - 9
     \]
   - The second line intersects the y-axis at \( y = 8 \) and has a negative slope. By counting grid units, it appears to fall by 2 for every 1 unit it moves to the right (slope of -2). This gives the equation:
     \[
     y = -2x + 8
     \]

2. **Determine the inequality symbols**:

   - The shaded region lies below the line \( y = 3x - 9 \), indicating an inequality of \( y \leq 3x - 9 \).
   - The shaded region also lies below the line \( y = -2x + 8 \), indicating an inequality of \( y \leq -2x + 8 \).

3. **Conclusion**: 

   The system of inequalities that represents the shaded region in the graph is:
   \[
   \begin{cases}
   y \leq 3x - 9 \\
   y \leq -2x + 8
   \end{cases}
   \]

Would you like further details or have questions about this solution?

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**Related Questions:**

1. How do you determine the slope of a line on a graph?
2. How does shading indicate the solution set of an inequality?
3. What are the steps to convert an inequality into its graph representation?
4. How would the inequality change if the shaded region were above the lines?
5. Why does changing the slope affect the direction of the line?

**Tip:** Always check the shading direction to identify which side of the line the inequality applies to.

Which system of linear inequalities is best represented by the graph?

Explore how to identify a system of linear inequalities from a graph. This example illustrates the use of slope-intercept form, shading direction, and inequalities, suitable for Grades 8-10.

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