This is the first of four lessons in the System of Equations unit. We are going to graph a system of equations in order to find the solution.
REMEMBER: A solution to a system of equations is the point where the lines intersect!
Prerequisites for completing this unit: Graphing using slope intercept form .
We will begin graphing systems of equations by looking at an example with both equations written in slope intercept form. This is the easiest type of problem!
Now we are going to look at a system of equations where only one of the equations is written in slope intercept form. The other equation is written in standard form.
So... what do you think we need to do first?
Now we will look at an example where there is no solution to the system of equations. Take note of what the graph looks like and why there might not be a solution.
Whenever two equations have the same slope they will be parallel lines. Parallel lines NEVER intersect. Therefore, the system of equations will NOT have a solution!
Our last example demonstrates two different things. The first is that there is more than one way to graph a system of equations that is written in standard form.
The second is that sometimes a system of equations is actually the same line, graphed on top of each other. In this case, you will see an infinite number of solutions. It may be helpful for you to review the lesson on using x and y intercepts for this example.
Did you notice that both equations had the same x and y intercept? This is because these two equations represent the same line. Therefore, one is graphed on top of the other. In this case, the system of equations has an infinite number of solutions! Every point on the line is a solution to both equations.
Now let's look at the other method for solving this system of equations. I am showing you both methods to remind you that you do have choices when solving a system of equations. There is more than one way to reach the solution.
Now you've seen two different ways to graph a system in standard form AND you've seen what happens when the equations are actually the same line!
Now you are ready to practice a few on your own.
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 © 2009-2014 Karin Hutchinson ALL RIGHTS RESERVED