So, what is a system of equations? This may be a new term for you if you are just beginning your study of Algebra.
A system of equations is a set of two or more equations that you deal with at one time. When solving the system, you must consider all of the equations involved and find a solution that satisfies all of the equations.
Dealing with more than one equation is what intimidates some students, but it's really not that hard.
This graph is an example of a System of Equations. These two linear graphs represent the cost of taking a cab around town based on the number of miles driven.
Since we are working with a system, we must graph both of the equations on the same graph.
When you graph a system, the point of intersection is the solution. The point of intersection on this graph is (3,8). That means that both companies will charge the same amount, $8 for 3 miles.
That is the only time that the two companies will charge the same amount. Therefore, the point (3,8) is the solution.
A linear system of equations will only have one solution, and that is the point of intersection. Although, as always, there are times when you will find no solution or an infinte number of solutions, and we will cover those special situations in the lessons below.
A system of equations can be solved using several different methods. This unit will teach you three different methods for solving a system of equations.
Below you will find all lessons and practice problems for Solving Systems of Equations. Click on the concept that you need help with or follow each lesson in the order presented for a complete study of Systems of Equations.