How do you graph the system of linear inequalities #y>=1# and #x<=6# and #y<2x-5#?
First, graph each inequality as a straight line. Remember to use a solid line for less/greater than or equal to inequalities, and a dashed line for less/greater than inequalities. You should end up with the following graph:
Labelling each possible region
A B C D E F
We have two choices here.
1. We could take a set coordinates in each region and test it with each of the inequalities, noting that they must satisfy all 3 inequities to be the desired region.
2. We can use the fact that, when we have more than two inequalities in a system, they will intersect to form a polygon. The polygon will have the same number of sides as there are inequalities. The area inside the polygon is the solution set to the system.
In this example the polygon is the triangle marked F