https://file.aiquickdraw.com/mathbot/file/17268134059299ie82hf2.jpg

The system of inequalities provided in the image is:

\[
\begin{aligned}
1. & \quad x > 2 \\
2. & \quad y \leq 7 \\
3. & \quad 2x + 3y \geq 6
\end{aligned}
\]

### Explanation:

1. **First Inequality: \(x > 2\)**  
   This inequality means that \(x\) must be greater than 2. On a graph, it represents a vertical boundary line at \(x = 2\), but the region is to the right of this line (since \(x > 2\)).

2. **Second Inequality: \(y \leq 7\)**  
   This inequality indicates that \(y\) is less than or equal to 7. On a graph, this is a horizontal boundary line at \(y = 7\), with the region below this line (including the boundary).

3. **Third Inequality: \(2x + 3y \geq 6\)**  
   This inequality represents a line with slope \(-\frac{2}{3}\) (since the equation of the line is \(2x + 3y = 6\)), and the region that lies above or on this line. 

### Graphical Representation:
To solve this system graphically, you would:
- Draw the line \(x = 2\) and shade the region to the right.
- Draw the line \(y = 7\) and shade the region below.
- Draw the line \(2x + 3y = 6\) and shade the region above it.

The solution to the system of inequalities is the overlapping region that satisfies all three conditions.

Would you like further details or help graphing this?

### 5 Related Questions:
1. How do you find the intersection point of two linear inequalities?
2. What is the meaning of the inequality \(2x + 3y \geq 6\)?
3. How can we represent solutions to inequalities graphically?
4. How would the solution change if the inequalities were strict, like \(x \geq 2\)?
5. What are boundary lines and how do they affect the solution in inequality problems?

### Tip:
When solving systems of inequalities, always identify boundary lines and determine whether the regions above or below these lines are included based on the inequality sign.

Solve the system of inequalities: x > 2, y ≤ 7, 2x + 3y ≥ 6.

Learn how to solve the system of inequalities x > 2, y ≤ 7, and 2x + 3y ≥ 6 by graphing. This example covers key algebraic concepts like inequalities, boundary lines, and graphical solutions. Suitable for students in Grades 9-10.

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