https://file.aiquickdraw.com/mathbot/file/1726794928941qerm0303.jpg

The question asks for the system of inequalities that defines the shaded region in the graph.

### Key observations:
- The graph has three boundary lines:
  1. A line passing through the points \( (0, 2) \) and \( (6, 0) \), which appears to be \( x + 3y = 6 \).
  2. A vertical line at \( x = 4 \).
  3. A line passing through \( (0, 1) \) and \( (1, 2) \), which appears to be \( y = x - 1 \).

### Steps to determine the correct system of inequalities:
1. **Line 1: \( x + 3y = 6 \)**
   - The region above this line is shaded, so the inequality is \( x + 3y \leq 6 \) (since we want the shaded area).
   
2. **Line 2: \( x = 4 \)**
   - The region to the left of this line is shaded, so the inequality is \( x \leq 4 \).
   
3. **Line 3: \( y = x - 1 \)**
   - The region above this line is shaded, so the inequality is \( y \geq x - 1 \), or equivalently, \( x - y \leq -1 \).

### Comparing with the options:
The system of inequalities that matches the observations is:
- \( x + 3y \leq 6 \)
- \( x - y \geq -1 \)
- \( x \leq 4 \)

This matches **Option E**.

Would you like further details or explanations? Here are some related questions for deeper understanding:

1. How do you find the equation of a line given two points?
2. What is the meaning of shading in inequality graphs?
3. How can you solve a system of inequalities graphically?
4. What happens if the inequalities are strict (e.g., \(<\) instead of \( \leq \))?
5. Can a system of inequalities have no solution? Why?

**Tip:** When working with inequalities, always test a point (like the origin) to see which side of the line should be shaded.

Sistem pertidaksamaan untuk daerah himpunan penyelesaian pada gambar berikut adalah....

Learn how to determine the system of inequalities for the shaded region of a graph. This problem involves linear equations and inequalities, such as x + 3y ≤ 6 and x - y ≥ -1, and tests your understanding of graphical solutions.

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