https://file.aiquickdraw.com/mathbot/file/1724755141863z3nzliix.jpg

Here is the graph of the system of linear inequalities you provided. The shaded region represents the solution set where all the inequalities overlap. Each boundary line corresponds to one of the inequalities, and the region that satisfies all inequalities is highlighted.

### Do you want more details or have any questions?
Here are five related questions you might explore:

1. How would the solution region change if one of the inequalities were strict (e.g., \( y \leq \frac{1}{2}x \))?
2. What are the coordinates of the vertices of the solution region?
3. How can we determine if a particular point lies within the solution region?
4. How do these inequalities relate to real-world problems, such as optimization or resource allocation?
5. Can we solve this system algebraically, and how would the algebraic solution relate to the graph?

### Tip:
When solving systems of inequalities, always check your work by substituting test points into the inequalities to verify which side of the boundary line should be shaded.

Explore how to draw a linear graph for a system of inequalities. Understand the shaded region representing the solution set and the boundary lines corresponding to each inequality. Learn related concepts such as linear graphs and systems of inequalities. Suitable for students in Grades 9-12.

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