# Linear Equations

The main focus of this book is how to solve general systems of linear equations. It also touches on matrices, but does not include more advanced topics in linear algebra, such as determinants, vector spaces, linear transformations, eigenvalues and eigenvectors.

This book is ideal for high school or first-year college students. A thorough knowledge of basic high school algebra is the only prerequisite.

## An Introduction to Linear Equations

Linear equations are the simplest type of algebraic equations. Examples of linear equations are 3x = 4, 5x + 2y = 10, and 2x y + 3z = 8. Linear equations may involve any number of variables, also called unknowns.

A single linear equation with a one variable has at most one solution. Most linear equations in one variable have one solution. An exception is a linear equation such as 0x = 4, which has no solutions.

Linear algebra is mainly concerned with solving systems of linear equations. An example of such a system is as follows:

3x + 2y = 7

4x y = 2

The above system of linear equations has a unique solution, namely x = 1; y = 2.