QUICK LINKS


Introduction

QUICK LINKS


Introduction

Solving Systems of Linear Equations by Graphing

INTRO
A system of linear equations is a set of two or more linear equations.
In this lesson, we focus on how to solve systems of linear equations by graphing, but we can also solve them .

When using the graphing method to solve a system of linear equations, we can imagine each equation as a path, and the solution is where the two paths intersect. ‘X’ marks the spot – try it out!

The graphing method can be broken down into two main parts: graphing each equation and finding the point where they intersect.

Consider the following system of equations:

If we graph the equations, we can see that they intersect at (, ):

We can check our answer by plugging the solution back into the system and making sure it checks out for both equations! 👌🏾

We typically see systems of linear equations with one solution, but they can also have no solutions or infinite solutions depending on if and how the lines intersect.

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CALCULATOR

Systems of Linear Equations Calculator

KEY STEPS

How to Solve a System of Linear Equations by Graphing

Step 1. Graph the first equation.

Writing the equation in slope-intercept form () can be helpful.

Step 2. Graph the second equation.

Writing the equation in slope-intercept form () can be helpful.

Step 3. Find the point where the two lines intercept.

The intersection point is the solution, and its - and -values should work for both equations.
If the lines , the system has one solution.
LESSON
The Graphing Method
PRACTICE
The Graphing Method
CONCLUSION
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