## Solving a System of Equations with Matrices

In section 2.2, you learned how to solve systems of equations in two variables using the Substitution Method or the Elimination Method. These methods worked well for problems involving two variables, but are cumbersome for problems involving more than two variables. Of course, problems involving more than two variables are what you are most likely to encounter in business and finance so we’ll need more efficient techniques involving matrices to solve these systems.

**Read **in Section 2.4

- What is a matrix?
- How do you form an augmented matrix from a system of linear equations?
- How do you use row operations to determine the reduced row echelon form of a matrix?
- Do all systems of linear equations have unique solutions?
- How do you mix different grades of ethanol to create a new grade of ethanol?

**Watch** Video Playlist

- Handout: How to Set Up and Solve an Application
- Handout: Solving a Dependent System Application
- Handout: rref Command on a TI Graphing Calculator
- Handout: Reduced Row Echelon Form on a TI Graphing Calculator
- Handout: Reduced Row Echelon Form in Excel or Google Sheets
- Handout: Set Up and Solve an Application on a TI Graphing Calculator with rref