MAC1105 §6.1 & §2.8 - Systems of Linear Equations and Absolute Value Functions

Vocabulary flashcards covering systems of linear equations, classification of systems, and absolute value equations and inequalities.

Consistent System

A system of equations that has at least one solution.

Inconsistent System

A system of equations that has no solution.

Independent System

A linear system of equations that has exactly one solution.

Dependent System

A linear system of equations that has infinitely many solutions.

Substitution Method

A method of solving a system of equations by solving one equation for $x$ or $y$, substituting the result into the other equation, and solving for the remaining variable.

Elimination Method

A method of solving a system of equations by multiplying one or both equations by constants so that variable terms are opposite in sign, then adding the equations so one variable vanishes.

Solution of a System of Linear Equations

An ordered pair $(x, y)$ that satisfies all equations in the given system simultaneously.

Absolute Value Equation

An equation containing an absolute value expression, which can be solved symbolically or graphically.

Absolute Value Inequality

An inequality containing an absolute value expression, with solutions expressed using inequality notation or interval notation.