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The question involves identifying which system of linear inequalities matches the graph displayed. The graph contains two shaded regions, one in red and the other in blue, which represent the solutions of two inequalities intersecting on the coordinate plane. 

Let's analyze each inequality:

1. **Red Shaded Region**: The boundary line is a solid red line that seems to be in a format similar to \( y \leq 2x - 1 \), as it slopes upward with a slope of 2 and y-intercept of -1.
   
2. **Blue Shaded Region**: The boundary line is a dashed blue line, which likely represents \( 4x + 3y \leq 18 \). This line has a negative slope and limits the blue shaded area.

Given the options:
- **A and C** have the inequality \( y < 2x - 1 \), which matches the red region boundary. 
- The inequality \( 4x + 3y \leq 18 \) in option C fits the blue region with its slope and boundary style.

Therefore, the correct answer is **Option C**.

Would you like a deeper explanation, or do you have further questions?

Here are five related questions to explore:
1. How can we determine the slope and intercept from an inequality’s graph?
2. What does a solid vs. dashed line mean in inequality graphs?
3. How do the inequality symbols (≤, ≥, <, >) affect shading?
4. How can we convert between standard form and slope-intercept form?
5. How can we test a point to see if it satisfies a given inequality?

**Tip**: To verify inequalities on a graph, pick a test point (e.g., (0,0)) and check if it satisfies the inequality.

Amber graphed a system of linear inequalities on the coordinate plane. Which system of linear inequalities is best represented by the graph?

Learn how to identify a system of linear inequalities from a graph with shaded regions and boundary lines. This problem explores key concepts in algebra, such as slope-intercept form, and uses graphing rules to determine the correct system of inequalities. Suitable for Grades 9-11 students.

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