Systems of Linear Equations

Climb into your car. Put on your seatbelt. Choose your destination and then…relax. That’s right — you don’t have to do anything else because you are in an autonomous car, or one that navigates its way to your destination. No cars are fully autonomous at the moment, so you still theoretically need to have your hands on the wheel. Self-driving cars may help ease traffic congestion, prevent accidents, and lower pollution. The technology is thanks to computer programmers who are developing software to control the navigation of the car. These programmers rely on their understanding of mathematics, including relationships between equations. In this chapter, you will learn how to solve systems of linear equations in different ways and use them to analyze real-world situations.

Sections

• Solve Systems of Linear Equations with Two Variables — determining whether an ordered pair is a solution of a system of equations, solving a system of linear equations by graphing, solving a system of equations by substitution, solving a system of equations by elimination, and choosing the most convenient method to solve a system of linear equations.
• Solve Applications with Systems of Equations — solving direct translation applications, geometry applications, and uniform motion applications with systems of equations.
• Solve Mixture Applications with Systems of Equations — solving mixture applications and interest applications with systems of equations.
• Solve Systems of Equations with Three Variables — determining whether an ordered triple is a solution of a system of three linear equations, solving a system of linear equations with three variables, and solving applications using systems of linear equations with three variables.
• Solve Systems of Equations Using Matrices — writing the augmented matrix for a system of equations, using row operations on a matrix, and solving systems of equations using matrices.
• Solve Systems of Equations Using Determinants — evaluating the determinant of a 2×2 matrix and a 3×3 matrix, using Cramer’s rule to solve systems of equations, and identifying inconsistent systems and systems with dependent equations.
• Graphing Systems of Linear Inequalities — determining whether an ordered pair is a solution of a system of linear inequalities and solving a system of linear inequalities by graphing.

This chapter overview is adapted from Intermediate Algebra 2e, Chapter 4 Introduction by Lynn Marecek and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.