https://file.aiquickdraw.com/mathbot/file/1728514655589iqpfjp7r.jpg

The graph represents a system of inequalities. The colored regions help identify the solution space where both inequalities are true. The goal is to determine which of the given points fall within this region.

Looking at the graph:

1. **The blue shaded region** represents one inequality, likely something like \(y \leq -x + 5\), as the blue shading is below a solid line.
2. **The orange shaded region** represents another inequality, probably \(y \geq x - 3\), with shading above the orange dashed line.

The solution space is where both shaded regions overlap, which is the triangular area near the origin.

### Let's evaluate each point:

1. **(1, 5)**: This point is above both shaded regions. It is not a solution.
2. **(-3, -4)**: This point is in the brown shaded area but outside the blue one. Not a solution.
3. **(2, -3)**: This point lies in the orange shaded region but not in the blue. Not a solution.
4. **(0, 2)**: This point is within the overlapping blue and orange regions. **This is a solution**.
5. **(-5, 2)**: This point is in the brown shaded area, outside the blue region. Not a solution.

### Conclusion:
The only correct solution is **(0, 2)**.

Would you like further details or explanations?

Here are five related questions for more practice:
1. What are the exact equations of the lines forming the boundaries of the shaded regions?
2. How do you determine which region to shade for an inequality?
3. Can inequalities have solutions on the boundary lines?
4. How would the solution set change if one of the inequalities was strict (e.g., \(<\) or \(>\) instead of \(\leq\) or \(\geq\))?
5. How would you graph a system of three inequalities?

**Tip:** Always pay close attention to whether the boundary line is solid (included) or dashed (not included) when interpreting inequalities.

A system of inequalities is shown on the graph. Select all the ordered pairs that are solutions to the system of inequalities.

Learn how to identify solutions to a system of inequalities using graphing techniques. This problem focuses on analyzing a system of two inequalities and determining the solution set by observing overlapping shaded regions. Suitable for students in Grades 8-10.

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