https://file.aiquickdraw.com/mathbot/file/1727655533712tqusl0h4.jpg

The problem in the image involves solving a system of two linear inequalities graphically. The first step asks to graph the solution set of the first inequality, which is given as:

\[
x > 2 \text{ or } y \geq 7
\]

Here’s how to approach it:

### Step-by-Step Explanation:

#### 1. **Graphing the Inequality \(x > 2\):**
   - The line \(x = 2\) is a vertical line, and since the inequality is \(x > 2\), the region to the right of this line needs to be shaded.
   - For the boundary:
     - The line is **dashed** because the inequality is strict (i.e., it does not include \(x = 2\)).
     - Enter two points on this vertical line, such as:
       - Point 1: \( (2, -10) \)
       - Point 2: \( (2, 10) \)
   - Select the region to the right of this line for shading (this will be the shaded region for \(x > 2\)).

#### 2. **Graphing the Inequality \(y \geq 7\):**
   - The line \(y = 7\) is a horizontal line.
   - The inequality \(y \geq 7\) includes the line, so the line should be **solid**.
   - The region above the line \(y = 7\) needs to be shaded.
   - Enter two points on this horizontal line, such as:
       - Point 1: \((-10, 7)\)
       - Point 2: \( (10, 7)\)

### Shading the Region:
- The solution to the system of inequalities involves the union of the regions for \(x > 2\) and \(y \geq 7\).
- For \(x > 2\), shade to the right of the dashed vertical line.
- For \(y \geq 7\), shade above the solid horizontal line.

Would you like further details on this or how to proceed with the graph?

Here are 5 related questions to expand on this:
1. How do you determine if a boundary line should be solid or dashed?
2. What is the difference between \(x > 2\) and \(x \geq 2\) in graphical terms?
3. How do you graph a compound inequality involving "or" versus "and"?
4. How do you find the intersection of two shaded regions for a system of inequalities?
5. What happens if the inequalities involve \(<\) or \(>\) for both \(x\) and \(y\)?

**Tip:** Always remember to label your boundary lines clearly and distinguish between dashed and solid lines for strict vs. inclusive inequalities.

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

Learn how to solve the system of linear inequalities x > 2 or y ≥ 7 graphically. This tutorial covers key algebraic concepts of inequalities, determining boundary lines, and shading regions. Suitable for students in Grades 8-10.

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