Hello! I see you're working on graphing the solution of a pair of linear inequalities. Let's tackle this step by step:
1. **Given Inequalities**:
- Inequality 1: \(x + y \leq 5\)
- Inequality 2: \(x \geq 3\)
2. **Graphing Inequality 1 (\(x + y \leq 5\))**:
- To graph this inequality, first change it to the equation of the line \(x + y = 5\).
- Plot this line as a dashed line because the inequality includes \(<\) not \(\leq\).
- Determine which side of the line to shade by choosing a test point (e.g., (0,0)).
- If the test point satisfies the inequality, shade that side. If not, shade the other side.
3. **Graphing Inequality 2 (\(x \geq 3\))**:
- For this inequality, graph the line \(x = 3\) as a solid line since it includes \(\geq\).
- Shade the side where \(x \geq 3\).
4. **Intersection or Union**:
- The intersection of the two shaded regions represents the solutions that satisfy both inequalities.
- The union would combine the shaded regions of both inequalities.
5. **Final Steps**:
- Identify the overlapping region if it exists for the intersection.
- If finding the union, shade the entire region covered by either inequality.
I hope this helps you understand how to graph the solutions of these linear inequalities. If you have any more questions or need further clarification, feel free to ask!
