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Graphing Systems of Equations

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!

Example 1

system of equations graph

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?

Example 2

solving systems of equations solving system of equations

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.

Example 3

system of equations problems


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.

Example 4

graphing a system of equations
solving a system of equations

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.

graphing a system using x and y intercepts

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!

Take a look at the questions that other students have submitted:

question and answers

Grpahing a vertical line

To ask a question, please visit my Math Forum.

Now you are ready to practice a few on your own.

system of equations practice problems

Click here to continue to Graphing Systems of Equations Practice Problems.

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