Solving 2x2 Systems of Equations by Graphing
Description/Explanation/Highlights
Video Description
This video explains how to solve a 2×2 system of equations by graphing. Please note: Watching the video will be helpful in seeing how the equations look when graphed on the coordinate plane.
Steps and Key Points to Remember
To solve a 2×2 system of equations by graphing, follow these steps:
- To solve a system of equations by graphing, carefully graph both equations on the coordinate plane.
- Graphing is usually easier if you change both equations into slope-intercept form.
- For example, to solve the system of equations: \(y=\frac{3}{2}x+2\) and \(y-3x=-1\), change the second equation to slope intercept by adding \(3x\) to both sides (or simply moving it to the right and changing signs) to get in slope intercept form, \(y=3x-1\).
- The solution to the system of equations is the intersection of the two lines on the graph.
- In the above example, the lines intersect at point \((2,5)\) so the solution to the system is \(x=2\) and \(y=5\).
- It is a good idea to check the solution when graphing due to potential graphing inaccuracies. To check, plug in the value of x and y to both equations to be sure both will make true statements.
- If you notice that the slopes of the lines are the same when you put them in slope/intercept form, the lines will be parallel and there will be no solution.
- Also, if the equations are the same when you put them in slope intercept form or you notice that the lines graph on top of each other, there are an infinite number of solutions.
- In the example, \(y=2x-1\) and \(y=2x+3\), the slope for both lines is 2 so there is no reason to graph it as we know the lines are parallel and there is no solution.
Here are some key points to keep in mind when solving a 2×2 system of equations by graphing.
- Use any method you would like to graph the lines but it may be easier to put both equations in slope/intercept form for ease of graphing.
- Using a calculator when available to graph may be more accurate.
- Use this method for equations that are easy to graph accurately to insure the intersection of the two equations is clear.
- The intersection of the two graphs is the solution.
- Check the accuracy of the graphs by plugging the solution into both equations to make sure it creates a true statement.
Video Highlights
- 00:00 Introduction
- 00:15 Solve the system, \(y=\frac{3}{2}x+2\) and \(y-3x=-1\) by graphing.
- 02:46 \(y=2x-1\) and \(y=2x+2\) example of lines with the same slope that will have no solution
- 04:10 \(y=5\) and \(y=-\frac{1}{3}x+3\) example of solving a system with a horizontal line by graphing
- 06:00 Conclusion
- To watch this video on YouTube in a new window with clickable highlights, click here