Solving Systems of Equations in Two Variable - Substitution

 When you are done with this section, you will be able to do the following

We are now moving on to a new topic of solving systems of equations.  It is often the case more than one type of information about a set of variables.  Often this information can be put together into multiple equations.  The "numbers" that cause all of these equations to be true at the same time are useful.  We are going to focus on a very special case of two equations with just two variables.  For example, the numbers that make both cost function and a revenue function equal to zero will let us know the "break even" point for the manufacture and sale of a particular item.

We are going to focus on one method of solving a system of equations at a time.  For this lesson, we are focusing on the method of substitution.

The main steps of the substitution method are:
1.  solve one of the two equations for one of the variables.
2.  replace that variable in the other equation with the expression found in step 1
3.  solve the equation found in step 2 for the only variable left
4.  plug that number or those numbers into either equation and solve for the other variable

The method of substitution can be used with both linear and non-linear equations.

When solving systems of equations, three things can happen.
1.  There is a finite set of solution points.
2.  There is an infinite set of solution points.
3.  There are no solution points.

If we think of these three possibilities in terms of the graphs of the equations the would correspond to
1.  The two graphs intersect in at least one point.
2.  The two graphs are the same graph.
3.  The two graphs do not intersect.




A good place to find information about solving systems of equations using the method of substitution is your text book (pages 448-449) in College Algebra 3rd edition by Stewart, Redlin, and Watson).

Additional Substitution Method On-line Resources:

Solving Systems of Equations in Two Variables - Substitution Homework:
The Solving Systems of Equations in Two Variables - Substitution Homework contains 5 problems.
Things to remember:
Homework examples:
    There are no homework example currently available for this homework set.
Keep in mind that it is recommended that you also complete all the problems in the set called "also recommended" with the same number as the Solving Systems of Equations - Substitution Homework.  There are many different ways to ask the same questions.  This will allow you to see additional problems that are related to this topic.

© 2005 Elizabeth E. K. Jones and the ASU Department of Mathematics and Statistics - All rights reserved.