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The shaded feasible region represents the solution to the system of inequalities:

1. \( x + y \geq 3 \) (blue region above the line)
2. \( 3x - y \geq 6 \) (green region below the line)
3. \( x + y < 8 \) (red region below the line)

The brown intersection area is the feasible region where all inequalities overlap. This is the region that satisfies all three conditions.

Let me know if you need further details or explanations!

Here are some related questions for deeper understanding:
1. How can you determine the coordinates of the vertices of the feasible region?
2. How do you solve a linear programming problem using this feasible region?
3. What would change if one of the inequalities was strict (e.g., \( x + y > 3 \))?
4. How do you interpret feasible regions in systems with more than two variables?
5. How can graphing software help in visualizing systems of inequalities?

**Tip:** When dealing with inequalities, always pay attention to whether the inequality is strict or non-strict (i.e., "<" vs. "≤"), as this changes the boundary condition.

Identify/Shade the feasible region for the following system of inequalities:
1. x + y ≥ 3
2. 3x - y ≥ 6
3. 2x + 2y < 16

Learn how to graph and identify the feasible region for a system of inequalities, including x + y ≥ 3, 3x - y ≥ 6, and 2x + 2y < 16. This lesson covers key concepts in graphing linear inequalities and finding the intersection where all conditions are satisfied.

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