To graph the system of linear inequalities:

1. $x \leq 5$: This inequality represents a vertical line at $x = 5$. The solution includes all points to the left of this line and on the line itself. It will be shaded to the left.

2. $y \geq -6$: This inequality represents a horizontal line at $y = -6$. The solution includes all points above this line and on the line itself. It will be shaded upwards.

To graph:

• Draw the vertical line $x = 5$. Shade everything to the left of this line.
• Draw the horizontal line $y = -6$. Shade everything above this line.
• The solution to the system is the region where both shadings overlap.

Would you like me to generate the graph for you?

Let me know if you have any questions or want additional explanations! Here are 5 related questions to extend your understanding:

1. How would the graph change if $x > 5$ instead of $x \leq 5$?
2. What happens if you change $y \geq -6$ to $y < -6$?
3. How do you graph a system with more than two inequalities?
4. What do the shaded regions represent in a system of inequalities?
5. Can two linear inequalities have no overlapping solution?

Tip: When graphing inequalities, dashed lines indicate that the boundary line is not included in the solution, while solid lines indicate that the boundary is included.