There are two ways to solve systems of equations without graphing. You can use the substitution method or linear combinations (which is also commonly known as the addition method).
This lesson is going to focus on using linear combinations, which is typically used when both equations are written in standard form.
The following steps are a guide for using Linear Combinations. Don't worry, it will make a lot more sense as we look at a few examples.
Ok... let's make these examples make sense by looking at some examples.
Our first example is the easiest example as it is already set up perfectly to use the linear combination method.
The next problem isn't set up so perfectly. It demonstrates the extra step that you need to take if your original problem doesn't have opposite terms. Look for that extra step.
The next problem requires two extra steps! This time, you need to rewrite both equations in order to create opposite terms.
Now, let's see what happens if our system of equations happens to be the same line.
Last example! We are going to see what happens when you try to use linear combinations to solve a system that has parallel lines.
Now, are you ready to practice a few problems on your own?Click here to go to the Combination Method Practice Problems.
Systems of Equations Unit
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 © 2009-2013 Karin Hutchinson ALL RIGHTS RESERVED