https://file.aiquickdraw.com/mathbot/file/17272318274434aktioc1.jpg

The system of inequalities provided is:

\[
\begin{cases}
y > 4x - 1 \\
y < \frac{1}{4}x - 2
\end{cases}
\]

### Analysis of the Graph:

- **First inequality**: \( y > 4x - 1 \)
    - The boundary line is \( y = 4x - 1 \), which is represented by the **dashed red line**. The shading above this line indicates that the inequality includes values where \( y \) is greater than the boundary.
  
- **Second inequality**: \( y < \frac{1}{4}x - 2 \)
    - The boundary line is \( y = \frac{1}{4}x - 2 \), which is represented by the **dashed blue line**. The shading below this line indicates that the inequality includes values where \( y \) is less than the boundary.

### Solution Region:
The overlapping region between the red and blue shading is the solution to this system of inequalities. Based on the graph, this region is a triangular section located near the negative x-values and negative y-values.

### Part 2: Coordinates of Three Points in the Solution Region
Three points that lie in the overlapping region (the solution to both inequalities) are:

1. \( (-2, -4) \)
2. \( (-3, -5) \)
3. \( (-4, -6) \)

These points are located in the dark purple region, where both inequalities hold true.

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Would you like more details on how the inequalities were graphed or how to solve similar systems?

### Five Related Questions:
1. How do you determine which side of the line to shade for an inequality?
2. What does the dashed line represent in a graph of inequalities?
3. How can you solve a system of inequalities algebraically instead of graphically?
4. How do you know when a point is a solution to a system of inequalities?
5. What would happen if one of the inequalities had a "greater than or equal to" sign?

### Tip:
When graphing inequalities, always check a point (like the origin) to confirm which side of the boundary line should be shaded.

Graph the system of inequalities and find three points that are solutions to the system.

Learn how to graph a system of linear inequalities and identify three solution points. This problem involves inequalities with two equations, focusing on shading regions and finding points within the solution area. Suitable for students in Grades 9-11.

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