The system of linear inequalities provided is:

$x \leq 5 \quad \text{and} \quad y \geq -8$

Step-by-Step Graphing:

1. First Inequality: $x \leq 5$

   • This represents all points to the left of (or on) the vertical line $x = 5$.
   • The boundary line will be $x = 5$, a vertical line at $x = 5$, and it will be solid because the inequality includes equality ("≤").
   • Shade the region to the left of this line, where $x \leq 5$.

2. Second Inequality: $y \geq -8$

   • This represents all points above (or on) the horizontal line $y = -8$.
   • The boundary line will be $y = -8$, a horizontal line at $y = -8$, and it will be solid because the inequality includes equality ("≥").
   • Shade the region above this line, where $y \geq -8$.

Graph Intersection:

• The solution to this system is the region where both shaded areas overlap.
• This is the area that lies to the left of the line $x = 5$ and above the line $y = -8$.
• The lines themselves are included in the solution because both inequalities are non-strict (≤ and ≥).

Would you like a detailed graph of this solution?

Here are 5 related questions for you:

1. What happens if one of the inequalities had been strict (e.g., $x < 5$ or $y > -8$)?
2. How do we interpret inequalities when both variables are involved (like $y > x + 2$)?
3. What is the significance of using solid vs. dashed boundary lines in graphing inequalities?
4. Can you find the area of the solution region if these inequalities bounded a specific shape?
5. How would you approach solving a system of inequalities with more than two conditions?

Tip: Always pay attention to whether the inequality includes equality (≤ or ≥) as it determines whether the boundary line should be solid or dashed.