https://file.aiquickdraw.com/mathbot/file/17269256247643oz9lli4.jpg

The image shows a system of inequalities for which we need to identify or shade the feasible region. Let's break down the problem step by step:

### Inequalities:
1. \( x + y \geq 3 \)  
   This is a straight line with equation \( x + y = 3 \), and the feasible region is above or on this line.

2. \( 3x - y \geq 6 \)  
   This line has equation \( 3x - y = 6 \), and the feasible region is below or on this line after rearranging it as \( y \leq 3x - 6 \).

3. \( 2x + 2y < 16 \)  
   Simplifying this, the equation becomes \( x + y < 8 \), which is a straight line with the region below it.

### Feasible Region:
The feasible region is the area where all three inequalities are satisfied. This can be determined by plotting the three boundary lines:
1. \( x + y = 3 \)
2. \( 3x - y = 6 \)
3. \( x + y = 8 \) (this is the simplified form of the third inequality)

The solution requires graphing these and finding the intersection of the shaded regions.

Would you like me to provide a sketch of the feasible region using these inequalities?

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

Learn how to identify and shade the feasible region for a system of linear inequalities involving x + y ≥ 3, 3x - y ≥ 6, and 2x + 2y < 16. This problem includes graphing each boundary line and finding the intersection of the shaded regions. Suitable for high school students in Grades 9-12.

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