https://file.aiquickdraw.com/mathbot/file/1727110689047oyjmney7.jpg

Looking at the graph provided, we can observe that the shaded region is bounded by two lines and specific constraints:

1. **Line 1 (y ≥ x + 1)**: This line has a slope of 1 and y-intercept at (0, 1), which forms the boundary of the shaded region on the left side. The shading is **above** this line, so the inequality would be \( y \geq x + 1 \).

2. **Line 2 (y ≤ 10)**: This is the horizontal line at \( y = 10 \) that forms the top boundary of the shaded region. The region is **below** this line, so the inequality would be \( y \leq 10 \).

3. **Constraint on x (x ≥ 0)**: The graph shows that the region is limited to the right of the y-axis, meaning \( x \geq 0 \).

### Therefore, the correct system of inequalities is:
- \( y \geq x + 1 \)
- \( y \leq 10 \)
- \( x \geq 0 \)

This matches **Option C**.

### Final Answer: **C. \( y \geq x + 1; y \leq 10; x \geq 0 \)**

Let me know if you want more details or if you have any questions!

Here are 5 related questions to expand on this:

1. How do you determine if a region is above or below a line in inequalities?
2. What does the inequality \( x \geq 0 \) represent in a graph?
3. How do boundary lines affect shading in inequalities?
4. Can a region be bounded by curves instead of straight lines? How would that change the inequalities?
5. How do you interpret a system of inequalities geometrically?

**Tip:** When graphing inequalities, use test points (like \( (0,0) \)) to check which side of the boundary should be shaded!

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

Explore how to solve a system of linear inequalities graphically, focusing on inequalities such as y ≥ x + 1, y ≤ 10, and x ≥ 0. This problem involves understanding boundary lines, shading, and regions, suitable for students in Grades 7-10.

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