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» » Substitution Method

Using the Substitution Method to
Solve Systems of Equations

The substitution method is one of two ways to solve systems of equations without graphing.

You might ask yourself, "Why wouldn't I just want to graph the equations to find the solution?" Well there are many reasons...

You may not have graph paper or an accurate way to graph the equations, thus making it hard to identify the solution.

Or, as the equations become more difficult, the solution is not always an identifiable point on the graph. This means that the solution may contain decimals or fractions, which is not easy to identify on a graph.

Once you learn the algebraic method for solving a system of equations, you will probably find that it becomes your preferred method. Graphing becomes too tedious.

The good news is that there are two methods, which makes this process easier depending on the problems you are given.

So, let's get to it!

The following steps can be used as a guide as you read through the examples for using the substitution method.

Steps for Using the Substitution Method in order to Solve Systems of Equations

  • Solve 1 equation for 1 variable. (Put in y =     or x =     form)

  • Substitute this expression into the other equation and solve for the missing variable.

  • Substitute your answer into the first equation and solve.

  • Check the solution.

These directions will make a lot more sense when you study the examples below.

Example 1

substitution method

The next example demonstrates a situation where it is easier to solve for x initially.

Example 2

using the substiution method

Let's take a look at another example. You'll find this very interesting! Pay close attention to the very last step of the solution.

Example 3

solving systems using the substitution method

Ok... one more unique example. Again, pay attention to the end result.

Example 4

substitution method

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