The elimination method is one of the most widely used techniques for solving systems of equations.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Why?
Because it enables us to eliminate or get rid of one of the variables, so we can solve a more simplified equation.
Some textbooks refer to the elimination method as the addition method or the method of linear combination.
This is because we are going to combine two equations with addition!
Here’s how it works.
First, we align each equation so that like variables are organized into columns.
Second, we eliminate a variable.
- If the coefficients of one variable are opposites, you add the equations to eliminate a variable, as Math Planet accurately states, and then solve.
- If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.
Thirdly, we substitute this value back into one of the original equations and solve for the other variable.
Simple!
Solve the System of Equations by the Elimination Method
What is really important to note is that we always add the equations – never subtract!
The reason is that addition is commutative, so no matter if we switch the order of the equations we will still arrive at an appropriate answer. Subtraction is not commutative, therefore could yield an incorrect result.
So always add!
Together we work through countless examples in detail, all while creating equivalent systems using the elimination method for solving systems of linear equations.
Elimination Method (How-To) – Video
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