Question

graph the solution to this system of inequalities.
( y geq -5 )
( x < -5 )
use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Graph \( y \geq -5 \)

The inequality \( y \geq -5 \) represents all points where the \( y \)-coordinate is greater than or equal to -5. This is a horizontal line passing through \( (0, -5) \). Since the inequality is "greater than or equal to", we draw a solid line (to include the line itself) and shade the region above the line (where \( y \) values are greater than -5).

Step2: Graph \( x < -5 \)

The inequality \( x < -5 \) represents all points where the \( x \)-coordinate is less than -5. This is a vertical line passing through \( (-5, 0) \). Since the inequality is "less than" (not "less than or equal to"), we draw a dashed line (to exclude the line itself) and shade the region to the left of the line (where \( x \) values are less than -5).

Step3: Find the Intersection

The solution to the system of inequalities is the region where both shadings overlap. This is the area that is above the line \( y = -5 \) (solid line) and to the left of the dashed line \( x = -5 \).

Answer:

The solution is the region above the horizontal solid line \( y = -5 \) and to the left of the vertical dashed line \( x = -5 \) in the coordinate plane. To graph it, draw a solid horizontal line at \( y = -5 \) and shade above it, draw a dashed vertical line at \( x = -5 \) and shade to the left of it, then the overlapping shaded region is the solution.