Questions and Answers
What does the term 'consistent' refer to in a system of equations?
What is the definition of 'dependent' in a system of equations?
What does the term 'dimension' refer to?
The number of rows, m, and the number of columns, n, of a matrix written m x n.
Define 'element' in the context of a set.
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What is 'elimination' in solving systems of equations?
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What does 'inconsistent' mean in a system of equations?
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What does 'independent' mean in a system of equations?
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What is 'substitution' in solving systems of equations?
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Define 'system of equations'.
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What is a 'system of inequalities'?
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Study Notes
Key Vocabulary in Algebra
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Consistent: Refers to a system of equations where there is at least one ordered pair satisfying both equations, indicating that the system has solutions.
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Dependent: Describes a system of equations that leads to an infinite number of solutions, meaning all solutions are shared by both equations in the system.
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Dimension: Indicates the structure of a matrix, defined by the number of rows (m) and columns (n), expressed in the format m x n.
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Element: Represents an individual object or number within a set, fundamental for understanding sets and their properties.
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Elimination: A method used in solving systems of equations where addition or subtraction is applied to remove one variable, simplifying the solution process.
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Inconsistent: Characterizes a system of equations that lacks any ordered pair solutions, meaning no point satisfies both equations simultaneously.
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Independent: Defines a system of equations that has exactly one distinct solution, highlighting a unique intersection point among the equations.
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Substitution: An algebraic technique used to find the precise solution of a system of equations by replacing variables with known values or expressions.
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System of Equations: Refers to a collection of two or more equations that share the same variables, commonly analyzed to find solutions that satisfy all equations in the set.
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System of Inequalities: A collection of two or more inequalities involving the same set of variables, used to analyze the relationships and constraints among variables.
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Description
Explore essential vocabulary from Chapter 6 of Glencoe Algebra 1. This quiz covers key terms related to systems of equations and matrices that are crucial for mastering this foundational algebra concept.
