# Systems of Linear Equations in Two Variables

There are two algebraic methods for solving systems of equations: the substitution method and the elimination method. In this section, we'll see how these specifically apply to systems where the equations are all linear. Then, finally, we'll look at some methods that are often included in textbook but that can't be relied on to consistently give accurate results.

# Video Lectures

Before we start talking about methods for solving systems of equations, I want to take a minute and be clear about what systems of equations are and what we mean by a solution to one. (lecture slides)

Substitution is the most straightforward of the methods for solving systems of equations but it isn't always the easiest. In this lecture, we'll look at the method and talk about when it's the best one to use. (lecture slides)

The elimination method for solving systems of equations is less straightforward than the substitution method but it has the advantage of being relatively easy to use with a wider range of systems. (lecture slides)

In this lecture, we're going to look at two special cases that come up with systems of equations: dependent systems where there are infinitely many solutions and inconsistent systems where there are no solutions. (lecture slides)

There are two methods, graphing and so-called numeric solutions, that you really should avoid. In this lecture, I'll go over both methods and why you can't rely on them. (lecture slides)