Podcast
Questions and Answers
What does the term 'consistent' refer to in a system of equations?
What does the term 'consistent' refer to in a system of equations?
- A system with at least one ordered pair that satisfies both equations (correct)
- A system with exactly one solution
- A system with infinite solutions
- A system with no solutions
What is the definition of 'dependent' in a system of equations?
What is the definition of 'dependent' in a system of equations?
- A system with an infinite number of solutions (correct)
- A system with at least one ordered pair that satisfies both equations
- A system with exactly one solution
- A system with no solutions
What does the term 'dimension' refer to?
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.
Define 'element' in the context of a set.
What is 'elimination' in solving systems of equations?
What is 'elimination' in solving systems of equations?
What does 'inconsistent' mean in a system of equations?
What does 'inconsistent' mean in a system of equations?
What does 'independent' mean in a system of equations?
What does 'independent' mean in a system of equations?
What is 'substitution' in solving systems of equations?
What is 'substitution' in solving systems of equations?
Define 'system of equations'.
Define 'system of equations'.
What is a 'system of inequalities'?
What is a 'system of inequalities'?
Flashcards
Consistent (system of equations)
Consistent (system of equations)
At least one ordered pair satisfies all equations.
Dependent (system of equations)
Dependent (system of equations)
Infinite solutions exist for all equations.
Dimension (of a matrix)
Dimension (of a matrix)
Number of rows (m) and columns (n) in a matrix: m x n.
Element (in a set)
Element (in a set)
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Elimination (in equations)
Elimination (in equations)
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Inconsistent System
Inconsistent System
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Independent System
Independent System
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Substitution (in equations)
Substitution (in equations)
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System of Equations
System of Equations
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System of Inequalities
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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