Systems of Equations
Overview
Expect to see some questions on the topic of Linear Systems on the SAT. In this section, we will review the following aspects of this topic:
 Definition of a Linear System
 Solving a Linear System
 Substitution Method
 Elimination Method
 Graphical Method
Let’s look at each of these in more detail:
Definition of a Linear System
A linear system involves two or more linear equations that represent graphs of linear functions. Where the graphs intersect is the solution to the system.
The kind of linear systems questions you will find on the SAT involve two variables. Here is an example of a linear system with the solution highlighted.
If a linear system doesn’t have a solution, that means the graphs of the lines are parallel.
Lines that are parallel have the same slope.
To learn more about the basics of linear systems, click on this link.
Solving a System Using the Substitution Method
In this section we go over the process of solving a linear system using the Substitution Method. This method is summarized below.

To see examples of solving systems using the Substitution Method, click on this link.
Solving a Linear System Using the Elimination Method
In this section we go over the process of solving a linear system using the Elimination Method. This method is summarized below.

To see examples of solving systems using the Elimination Method, click on this link.
Solving a System Using a Graphical Approach
In this section we go over the process of solving a linear system using the Graphical Method. This method is summarized below.

To see examples of solving linear systems by graphing, click on this link.
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