Also in this series:

• Lesson 1: Introduction
• Lesson 2: Graphing (current page)
• Lesson 3: Elimination
• Lesson 4: Substitution

Welcome to Your Tutor Online video lessons. Today we continue with the second video in our four part series on solving systems of linear equations. In this lesson we’ll look at solving systems by graphing. Now, this is the easiest, but also the most time consuming method of solving systems. You have to re-arrange the equations into a graph-able form; set up a graph; plot some points; and then find out if the intersect or not. All you need to do is graph the two equations you are given on the same coordinate plan. If you need a refresher on this you can look over my previous lesson on graphing equations.

As discussion in the introduction: if the lines intersect then the point of intersection is the solution, if they are parallel then there is no solution, and if they happen to be the same line then there are infinite solutions.

Lets look at just one example: 3x + 2y = 6 and 4x - 3y = 12. I prefer to work with slope-intercept for so I’ll go ahead and re-write each equation.

So our new equations, after we put them in slope-intercept form, are y = - (3/2)x + 3 and y = (4/3)x - 4. Now we just need to graph these two equations on the same coordinate plane.

We’ll start with y = - (3/2)x + 3. We’ll start at the y intercept, +3, so go up 3 on the y axis. And then we’ll use the slope to get a couple other points on the line. Down 3 and over 2. And we will go one more time. That’s enough points, now we just need to connect the dots and we have our line.

For the other equation we are going to go to the y intercept first, -4, and put a dot. Are we are going to rise 4 and run 3. And we’ll connect those dots.

The two lines intersect, and the point where they intersect will be our solution. In this case it’s not whole numbers but that’s okay, you can give an estimate. And this looks to be 2.5 and -0.5. Your teacher may have his or her own requirements for rounding or guessing if this particular situation comes up.

I hope you found this lesson useful. If you have any questions leave a comment on the blog at www.YourTutorOnline.com If you have any lesson suggestions send an email to podcast@yourtutoronline.com Thanks for watching, class dismissed.

This entry was posted on Thursday, October 16th, 2008 at 9:07 pm and is filed under Algebra. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.