https://file.aiquickdraw.com/mathbot/file/17273567079755z6mfdjp.jpg

Let's break down the graph to find which system of inequalities produces the shaded region.

### Step 1: Analyze the boundary lines.
- There are two boundary lines in the graph:
  1. A solid line with a negative slope. This line seems to be \( y = -x + 4 \).
     - Since the line is solid, the inequality includes the boundary, i.e., \( y \leq -x + 4 \).
     - The region is shaded below this line, confirming that the inequality involves \( \leq \).
  
  2. A dashed line with a positive slope. This line appears to be \( y = x + 2 \).
     - The line is dashed, meaning the inequality does not include the boundary, i.e., \( y < x + 2 \).
     - The region is shaded below this line, so the inequality is \( y < x + 2 \).

### Step 2: Identify the region.
The region shaded in the graph is below both lines. This implies that both inequalities must hold simultaneously.

### Step 3: Conclusion.
From the graph, the system of inequalities representing the shaded region is:
- \( y \leq -x + 4 \)
- \( y < x + 2 \)

Now, checking the options:
- **Option C**: \( y \leq -x + 4 \) and \( y < x + 2 \) is the correct answer.

### Would you like further clarification, or do you have any questions?

Here are 5 related questions you can explore:
1. How do you determine the equation of a line from a graph?
2. What is the difference between dashed and solid lines in graphing inequalities?
3. How do you graph a system of inequalities on the coordinate plane?
4. How would the region change if the inequality was \( y \geq -x + 4 \)?
5. What happens when two inequalities share the same boundary line?

**Tip**: Always pay attention to whether a boundary line is solid or dashed, as it indicates whether the points on the line are included in the solution!

Which of the following systems of inequalities would produce the region indicated on the graph below?

Learn how to determine the correct system of inequalities for a shaded region on a graph. This problem covers key algebraic concepts like graphing inequalities and understanding boundary lines. Suitable for students in Grades 9-11.

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