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 \( y \geq -5 \)

For the inequality \( y \geq -5 \), we first draw the horizontal line \( y = -5 \). Since the inequality is "greater than or equal to", the line should be solid. Then, we shade the region above the line (because \( y \) values greater than or equal to -5 are above \( y = -5 \)).

Step2: Graph \( x < -5 \)

For the inequality \( x < -5 \), we draw the vertical line \( x = -5 \). Since the inequality is "less than" (not "less than or equal to"), the line should be dashed. Then, we shade the region to the left of the line \( x = -5 \) (because \( x \) values less than -5 are to the left of \( x = -5 \)).

Step3: Find the Intersection

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

Answer:

The graph consists of a solid horizontal line at \( y = -5 \) with the region above it shaded, and a dashed vertical line at \( x = -5 \) with the region to the left of it shaded. The overlapping region (above \( y = -5 \) and left of \( x = -5 \)) is the solution. (Note: Since this is a graphing problem, the final answer is the described graph. If using a graphing tool, plot the solid line \( y = -5 \), shade above it, plot the dashed line \( x = -5 \), shade left of it, and the intersection is the solution region.)