Key Words & Definitions
1) What is a Variable?
Answer: A variable represents something we wish to find.
Below are some examples of defining a variable:
Example 1: Let g = the number of people wearing gloves when the weather is cold
Let n = the number of people not wearing gloves when the weather is cold
Example 2: Let c = the number of people who bring coffee to class
Let p = the number of people who do not bring coffee to class
Example 3: Let w = the number of people wearing a wristwatch
Let x = the number of people not wearing a wristwatch
2) What is an equation?
Answer: An equation contains one or more variables.
Below are a few examples of equations. The variables are defined according to the examples in question number one.
Example 1: g+ n = total number of people observed
Example 2: c + p = total number of people observed
Example 3: w + x = total number of people observed
Note: An equation will appear in many different forms than those listed above.
3) What is a system of equations?
Answer: A system of equations contains two or more equations in a problem.
Below are some examples of a system of equations.
4) What is the purpose/reason for having a system of equations?
Answer: The purpose is to find a value(s) for each variable that satisfies the set of equations. These value(s) are called a solution set.
5) How many different types of solutions to a system of equations are possible?
Answer: Three types of solutions will be covered in this course.
| Solutions | What the solution means |
| Only one solution is found for the system | The equations in the system intersect at only one point |
| Infinite solutions | The equations contained in the system are all the same |
| No Solution | The equations in the system do not intersect. |