How do you graph the system of inequalities #y≥ -5# and #x≥6#?

Question

How do you graph the system of inequalities #y≥ -5#  and #x≥6#?

Kennedy Adams · Accepted Answer

Lets start by graphing #y>=-5# First graph #y = -5# line. The inequality includes #-5# so our line will be a solid line, not a dashed line. Then take a random point (#y#-axis #!= -5#), lets say #(0,0)#. This point satisfies the inequality so we will shade our line's side which includes #(0,0)#.
The resulting graph should look like this: graph{y >= -5 [-10, 10, -20, 20]}  Now lets graph #x>=6# In order to graph this inequality we need to graph the #x=6# line.
Since the inequality includes #6#, our line will be a solid line. Lets take a random point to determine which part will be shaded. #(7,0)#
#7>=6# satisfied. So the part of the coordinate plane where #(7,0)# lies will be shaded.
The graph will look like this: graph{x>=6 [-10, 10, -20, 20]} Now, there is an area which is shaded by both graphs. That area is the result of this problem. Because it means both inequalities are satisfied in that area.

Eli Assouline · Answer

undefined To graph the system of inequalities $ y \geq -5 $ and $ x \geq 6 $, you would draw two lines. For $ y \geq -5 $, you would draw a horizontal line at $ y = -5 $ and shade the area above the line because it includes all values greater than or equal to -5. For $ x \geq 6 $, you would draw a vertical line at $ x = 6 $ and shade the area to the right of the line because it includes all values greater than or equal to 6. The shaded region where both inequalities overlap represents the solution space for the system.