A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.

The equations in the system can be linear or non-linear. This tutorial reviews systems of linear equations.

A problem can be expressed in narrative form or the problem can be expressed in algebraic form.

Work the following problems. Click on Solution, if you want to review the solutions.

Problem 2.1a:

        A total of $12,000 is invested in two funds paying 9% and 11% simple interest. If the yearly interest is $1,180, how much of the $12,000 is invested at 9% and how much is invested at 11%?          Solution

Problem 2.1b:

        An airplane flying into a headwind travels the 1800-mile flying distance between two cities in 3 hours and 36 minutes. On the return flight, the same distance is traveled in 3 hours. Find the ground speed of the plane and the speed of the wind, assuming that both remain constant.         Solution

Problem 2.1c:

        Ten gallons of a 30% acid mixture is obtained by mixing a 20% solution with a 50% solution. How much of each must be used?          Solution

Problem 2.1d:

         Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many of each kind of ticket were sold?         Solution

Problem 2.1e:

        Solve for x and y in the following system of equations.


Problem 2.1f:        Solve for x and y in the following system of equations.


If you would like to return to the beginning of the two by two system of equations, click on Example.

If you would like to test yourself by working some problem similar to this example, click on Problem.

This site was built to accommodate the needs of students. The topics and problems are what students ask for. We ask students to help in the editing so that future viewers will access a cleaner site. If you feel that some of the material in this section is ambiguous or needs more clarification, or if you find a mistake, please let us know by e-mail at

[Next Problem]
[Three-Variable Systems]
[Algebra] [Geometry] [Trigonometry ]

S.O.S MATH: Home Page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author: Nancy Marcus

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour