Graph the solution set of the system of inequalities.
x-y>3                                                                                                                                                                      5+y≤2x                                              

Here is the graph of the system of inequalities:

- The blue dashed line represents \( y = x - 3 \), with the solution region shaded below it.
- The red dashed line represents \( y = 2x - 5 \), with the solution region shaded below or on this line.

The overlapping shaded region is the solution set for the system of inequalities.

Would you like more details on the graph or have any questions?

Here are 5 related questions to explore further:

1. How do you determine whether to shade above or below a boundary line for an inequality?
2. What happens when the inequality symbol changes to "≥" or "≤" in graphing?
3. How would the graph change if the inequalities involved vertical or horizontal lines?
4. How can you find the exact coordinates of the intersection point of the two lines?
5. How do systems of inequalities relate to linear programming?

**Tip:** When graphing inequalities, always use dashed lines for strict inequalities (>, <) and solid lines for inclusive inequalities (≥, ≤).

Graph the solution set of the system of inequalities: x - y > 3, 5 + y ≤ 2x.

Explore how to graph the solution set of the system of inequalities x - y > 3 and 5 + y ≤ 2x. This problem covers key concepts such as graphing linear inequalities, understanding solution regions, and identifying the intersection of inequalities. Suitable for Grades 9-12 students.

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