Solving Systems of Equations
Using Linear Combinations

There are two ways to solve systems of equations without graphing. You can use the substitution method or linear combinations.

This lesson is going to focus on using linear combinations.

The following steps are a guide for using Linear Combinations. Don't worry, it will make a lot more sense as we look at a few examples.

Steps for Using Linear Combinations

Arrange the equations with like terms in columns.

Analyze the coefficients of x or y. Multiply one or both equations by an appropriate number to obtain new coefficients that are opposites

Add the equations and solve for the remaining variable.

Substitute the value into either equation and solve.

Check the solution.

Ok... let's make these examples make sense by looking at some examples.

Example 1

The next problem demonstrates the extra step that you need to take if your original problem doesn't have opposite terms! Look for that extra step!

Example 2

linear combinations

The next problem requires two extra steps! This time, you need to rewrite both equations in order to create opposite terms!

Example 3

Let's see what happens if our system of equations happens to be the same line!

Example 4

linear combinations

Last example! We are going to see what happens when you try to use linear combinations to solve a system that has parallel lines!

Example 5

linear combinations

Now, are you ready to practice a few problems on your own?Click here to go to the Combination Method Practice Problems.

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Systems of Equations Unit

Solving a System of Equations Using a Graph

Using a Graph Practice

Using the Substitution Method

Substitution Method Practice

Using Linear Combinations (Addition Method)

Linear Combinations Practice

Systems of Equations Word Problems

Word Problems Practice

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