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Mathematics LibreTexts

7: Systems of Equations

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In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linear and nonlinear, and then partial fractions.

  • 7.1: Systems of Linear Equations - Two Variables
    A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution.
  • 7.2: Systems of Linear Equations - Three Variables
    https://math.libretexts.org/TextMaps/Algebra_Textmaps/Map%3A_Elementary_Algebra_(OpenStax)/11%3A_Systems_of_Equations_and_Inequalities/11.3%3A_Systems_of_Linear_Equations%3A_Three_Variables
  • 7.3: Partial Fractions
    Decompose a ratio of polynomials by writing the partial fractions. Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to each other, then setting up and solving a system of equations. The decomposition with repeated linear factors must account for the factors of the denominator in increasing powers. The decomposition with a nonrepeated irreducible quadratic factor needs a linear numerator over the quadratic factor.
  • 7.4: Solve Systems of Equations Using Matrices
  • 7.5: Graphing Systems of Linear Inequalities

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This page titled 7: Systems of Equations is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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