### Unit 6: Systems of Linear Equations and Inequalities

You have seen in Units 2 and 5 that linear equations in one variable usually have 1 solution and linear equations in two variables have infinitely many solutions. What would happen if two linear equations in two variables had to be solved together? That would mean that a pair of numbers would have to satisfy both equations at the same time. This pair of numbers would be the solution of a system of linear equations. Some of the mixture problems from Unit 3 could be solved by setting up a system of linear equations, because they involve two given relationships between two variables. In this unit, you will learn three different methods of solving systems of linear equations and use them to solve a variety of world problems. You will also find solutions of systems of linear inequalities in two variables and to apply them to real-life situations. For example, if you want to determine the price for and amount of two types of candy for a party, you have the constraints of the total amount of candy needed (GREATER than a given amount) and the amount of money you can spend (LESS than the amount you have). The quantities of two types of candy you buy have to satisfy both constraints. In this unit, you will learn how to identify all the possibilities for similar problems.

**Completing this unit should take you approximately 18 hours.**