This post will take a look at an algebraic concept, system of equations. A system of equations is a set of equations or an equation system that is related by a common solution.

Table of Contents

## What is the System of Equations

This post is specifically looking at linear sets of equations and systems of equations. A linear system of equations is a set of linear equations that may share an infinite or a single unique solution. Some linear equations share no solution at all. A solution to a linear set of equations is an ordered pair that satisfy all equations in the system at the same time.

## Types of Solutions for Linear System of Equations

A liner system of equations have three possible types of solutions:

The system has infinite solutions, all ordered pairs are solutions to each equation in the solution.

The system has no solution. There is no ordered pair that will satisfy all the equations in the system.

The system has a single unique solution (most system of equation problems that you will see in your math class will be in this category). One set of ordered pairs will satisfy all the equations in the system.

## Examples of Infinite Solutions

Here is an example of a system of equations with infinite solutions in a graph.

## Examples of No Solutions

Here is an example of a system of equations with no solutions in a graph.

## Examples of Single Unique Solutions

Here is an example of a system of equations with a single and unique solution in a graph.

Linear Relationships in Tables

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