Related Topics:
More Lessons for Algebra
Math Worksheets
Examples, solutions, videos, worksheets, games, and activities to help Algebra 1 students learn how to solve systems of linear equations using the elimination method or addition method.
Solving Systems of Equations Using the Elimination Method (or Addition Method) The Elimination Method (also known as the Addition Method) is a powerful technique for solving systems of linear equations. The core idea is to manipulate the equations in a way that allows you to eliminate (cancel out) one of the variables when you add or subtract the equations. This leaves you with a single equation that has only one variable, which is then easy to solve.
The following diagram shows an example of solving systems of equations by elimination by addition. Scroll down the page for more examples and solutions of solving systems of equations.
Algebra Worksheets
Practice your skills with the following worksheets:
Printable & Online Algebra Worksheets
Steps to Solve a System of Equations Using Elimination:
Special Cases in Elimination
Sometimes, when using the elimination method, both variables might cancel out.
Case A: No Solution (Inconsistent System)
If, after adding the equations, both variables cancel out and you are left with a false statement (e.g., 0=5 or 3=−2), then the system has no solution. This means the lines are parallel and never intersect.
Case B: Infinitely Many Solutions (Consistent and Dependent System)
If, after adding the equations, both variables cancel out and you are left with a true statement (e.g., 0=0 or 7=7), then the system has infinitely many solutions. This means the two equations represent the exact same line.
Videos
Solving Systems of Equations… Elimination Method
How to use the elimination method to solve a system of linear equations (simultaneous equations)?
Example 1: where terms cancel right away when you add the equations.
Example 2: Multiply one equation by a number before adding the equations
Example 3: Multiply both equations by numbers before adding.
Example 4: How to subtract equations instead of adding them.
How to Solve Systems of Equations Using Elimination By Addition?
Solving Systems of Equations
Students learn to solve a system of linear equations by addition
To solve a system of equations by addition, the goal is to cancel out one of the variables by adding the equations together. Students may need to multiply one or both of the equations by a number in order to set up a situation where one of the variables will cancel out when the equations are added together.
Solving a system of two equations in two variables by the addition method
Solving Systems of Linear Equations Using Elimination By Addition
Two complete examples and part of a third problem are shown!
Solve Systems of Linear Equations by Elimination
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.