Application Problems Involving Systems of Two Equations and Two Variables

Many applied problems involve more than one unknown quantity. Although some problems with two unknowns can be solved using just one variable, it is often easier to use two variables.

To solve a problem with two unknowns, we must write two equations that relate the unknown quantities. The system formed by the pair of equations can then be solved using the methods of this chapter.

Now that you are familiar with the algebraic methods (substitution and elimination) for solving systems of equations, you can use these methods to solve word problems. To solve all of the application problems in this section, it is necessary to:

Steps for Solving All Application Problems with Systems of Equations

1. Define both variables you will be solving for.
2. Write a system of two equations to solve.
3. Use either elimination or substitution to solve the system of equations.
4. Use sentence(s) to state your answer, and include units in your answer, when applicable.

As you go through problems you will begin to see that many problems follow certain patterns or fall into specific categories. It is useful to start to learn these types of problems, as recognizing the type of problem you are solving can make setting it up more straightforward. The next few pages will show examples of some of the different types of problems that can be solved using systems of linear equations.