Question

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

Answer 1

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.