Why It Matters: Systems of Equations and Inequalities
After years of saving, you have finally done it—you rented a space to open your very own coffee shop. You’ve already painted the walls and set up the furniture. The next step is to plan your menu. In considering both taste and cost, you have developed a coffee flavor that is sure to bring customers coming back for more.![Photo shows the interior of a coffee shop with a counter in the background, and tables and chairs in the forefront.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1746/2017/04/19191401/cafe-2081857_1920-300x225.jpg)
You can also relate the cost of each type of bean to the cost of the mixture. The cost of the first type of coffee bean is the number of pounds times the cost per pound, . Similarly, cost of the second type of coffee bean is the number of pounds times its cost per pound, . And the total cost is $980 for 100 pounds.
Now you have two equations, but what can you do to solve for the values of and ? And what information do those values give you? To find the answers to these and other questions, read on in this module. There you will learn about combinations of equations, called systems of equations, along with different methods of solving them.
Learning Objectives
Systems of Linear Equations: Two Variables- Solve systems of equations by graphing, substitution, and addition
- Identify inconsistent systems of equations containing two variables
- Express the solution of a system of dependent equations containing two variables using standard notations
Systems of Nonlinear Equations and Inequalities
- Solve a system of nonlinear equations using substitution or elimination
- Graph a nonlinear inequality
- Graph a system of nonlinear inequalities
Systems of Linear Equations: Three Variables
- Solve systems of three equations in three variables
- Identify inconsistent systems of equations containing three variables
- Express the solution of a system of dependent equations containing three variables using standard notations
Partial Fractions: an Application of Systems
- Decompose , where has only nonrepeated linear factors
- Decompose , where has repeated linear factors
- Decompose , where has a nonrepeated irreducible quadratic factor
- Decompose , where has a repeated irreducible quadratic factor