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Understanding Systems of Equations and Inequalities in Algebra

This unit explores the fundamentals of systems of equations, which consist of two or more equations that need to be solved simultaneously. We define terms such as a solution of a system, which is an ordered pair (x, y) satisfying all equations, and identify different types of systems, including inconsistent, independent, dependent, and consistent systems. Additionally, we cover systems of inequalities and their solution sets. This overview provides students with a solid foundation in solving systems in algebra.

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Understanding Systems of Equations and Inequalities in Algebra

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  1. Introductory AlgebraGlossary Unit Seven

  2. system of equations • Two or more equations to be solved at the same time.

  3. solution of a system • An ordered pair (x, y) that makes both equations true at the same time.

  4. inconsistent system • A system with no solution.

  5. independent equations • Equations of a system that have different graphs.

  6. dependent equations • Equations of a system that have the same graph (because they are different forms of the same equation).

  7. consistent system • A system of equations with a solution.

  8. system of inequalities • Two or more inequalities to be solved at the same time.

  9. solution set of a system of linear inequalities • All ordered pairs that make all inequalities of the system true at the same time.

  10. Return toIntroductory Algebra • Created by • James Q. Jacobs

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