Systems of Linear Equations
An architect designing a home may have restrictions on both the area and perimeter of the windows because of energy and structural concerns. The length and width chosen for each window would have to satisfy two equations: one for the area and the other for the perimeter. Similarly, a banker may have a fixed amount of money to put into two investment funds. A restaurant owner may want to increase profits, but in order to do that he will need to hire more staff. A job applicant may compare salary and costs of commuting for two job offers. This chapter looks at methods to solve situations like these using equations with two variables.
Sections
- Solve Systems of Equations by Graphing — determining whether an ordered pair is a solution of a system of equations, solving a system of linear equations by graphing, determining the number of solutions of a linear system, and solving applications of systems of equations by graphing.
- Solving Systems of Equations by Substitution — solving a system of equations by substitution and solving applications of systems of equations by substitution.
- Solve Systems of Equations by Elimination — solving a system of equations by elimination and solving applications of systems of equations by elimination.
- Solve Applications with Systems of Equations — solving direct translation, geometry, uniform motion, and mixture applications with systems of equations.
- Solve Mixture Applications with Systems of Equations — solving coin-value and ticket-value mixture applications, and mixture applications involving mixing two solutions of different concentrations.
- 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 Elementary Algebra 2e, Chapter 5 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, 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.