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

Apr 2, 2015

Lets start by graphing $y \ge - 5$

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 $\ne - 5$), lets say $\left(0 , 0\right)$. This point satisfies the inequality so we will shade our line's side which includes $\left(0 , 0\right)$.
The resulting graph should look like this:

graph{y >= -5 [-10, 10, -20, 20]}

Now lets graph $x \ge 6$

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.

$\left(7 , 0\right)$
$7 \ge 6$ satisfied.

So the part of the coordinate plane where $\left(7 , 0\right)$ 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.