What is a system of inequalities? A system of inequalities is two or more inequalities that pertain to the same problem. In order to solve the system, we will need to graph two inequalities on the same graph and then be able to identify the areas of intersection on the graph.
Take a look at a graph for a system of inequalities and then we will walk through a few examples step-by-step.
Notice how we still use solid and dotted boundary lines based on the inequality symbol. You will also use a test point and shade the half plane that contains all solutions, just as we discussed in the graphing inequalities lesson.
The only difference for this lesson will be that we must graph two inequalities on the same graph and then identify the area shaded by BOTH inequalities.
Let's take a look at our first example and this will make more sense.
Not too bad, is it? It might help for you to have two different colored pencils if you are practicing along with me. If you don't have colored pencils, then you can draw horizontal lines for one inequality and vertical lines for the other. This will make it easier to see which area contains solutions for both inequalities.
The next example will demonstrate how to graph a horizontal and a vertical line.
Example number two may have looked confusing at first because of the inequalities.
Remember that a horizontal line is always graphed when the equation or inequality begins with y = "a constant". A vertical line is always graphed when the equation or inequality begins with x = "a constant". Horizontal and vertical lines only have 1 variable.
Use this solver to help with graphing systems of inequalities.
Sign Up for Algebra Class E-courses
"I'd like to start off by relaying my sincerest gratitude for your dedication in teaching algebra. Your methodology is by far the simplest to follow, primarily because you take the time to include the small steps in between that most other teachers leave out.
It helps to know why you are doing something. I am 45 and heading to college to get my BS in Business. I need to brush up, hence the visit to your site. Great Job!"
Jimmy - United States
"I stumbled onto your site after I found out that I needed to use some fundamental algebra for an assignment. Turns out I had forgotten some things and your great site helped me remember them like "that" (snap of fingers). The organization of the site let me find exactly what I was looking for so easily. Kudos to you for maintaining such a great resource for students of all ages!"
Tom - United States
"I just wanted to write and basically thank you for making such a wonderful website! I'm 20 years old and about to take a basic placement test for college. I wanted to brush up on my Algebra skills and I stumbled upon your site. I'm amazed at how simple you make it and how fast I'm remembering Algebra! I don't remember getting most of the answers right when I had an actual teacher in front of me teaching this. Thanks a lot!"
Elizabeth - United States
"I am a pensioner living in South Africa. I stumbled on your website, the best thing that could ever happen to me! Your course in Algebra has helped me a lot to better understand the different concepts. Thank you very much for sharing your skills for teaching math to even people like me. Please do not stop, as I am sure that your teachings have helped thousands of people like me all over the world."
Noel - South Africa
This is an amazing program. In one weekend I used it to teach my Grade 9 daughter most of the introductory topics in Linear Relations. I took her up to Rate of Change and now she can do her homework by herself.
Reg - United States
Copyright © 2009-2014 Karin Hutchinson ALL RIGHTS RESERVED