https://file.aiquickdraw.com/mathbot/file/1727655647355gfnz77dz.jpg

The system of linear inequalities given is:
\[
x > 2 \quad \text{or} \quad y \geq 7
\]

To analyze this, let's break down each inequality:

1. **For \( x > 2 \)**:
   - This represents a vertical line at \( x = 2 \), but since \( x > 2 \), the shading is to the right of this line. The line itself is dashed because the inequality is strict (\(>\)).

2. **For \( y \geq 7 \)**:
   - This represents a horizontal line at \( y = 7 \). Since the inequality is \( y \geq 7 \), the region above this line (including the line itself) is shaded. The line is solid because the inequality includes equality (\( \geq \)).

Since the problem asks for the combined solution set using "or," we are looking for the **union** of these two regions. This means any point that satisfies either \( x > 2 \) or \( y \geq 7 \) should be part of the solution set.

### Therefore, the correct choice is:
- **The union of the individual solution sets**.

Would you like me to explain further or proceed with more details?

### 5 Related Questions:
1. How would the graph change if the inequality were \( x \leq 2 \) instead of \( x > 2 \)?
2. What is the difference between the union and intersection of solution sets?
3. How do you graph inequalities that involve "and" instead of "or"?
4. What if both inequalities were strict (e.g., \( x > 2 \) and \( y > 7 \))? How would that affect the graph?
5. How do you determine if a point satisfies a given system of inequalities?

### Tip
When graphing inequalities, always use a dashed line for strict inequalities (\(<\) or \(>\)) and a solid line for inequalities that include equality (\( \leq \) or \( \geq \)).

Solve the system of two linear inequalities graphically: x > 2 or y ≥ 7

Learn how to solve and graph the system of two linear inequalities x > 2 or y ≥ 7. This lesson covers how to represent inequalities graphically on a coordinate plane, including dashed and solid lines for strict and inclusive inequalities. Suitable for students in Grades 8-10.

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