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Questions and Answers
What is the definition of intersection?
What is a linear equation?
An equation whose graph is a straight line.
What is a system in mathematics?
A group of similar and related elements considered together.
What is the solution of a linear equation?
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Substitution is a method of solving systems of linear equations by ______.
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What is Gaussian elimination?
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What does it mean for lines to coincide?
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What is a consistent system?
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What is a dependent system?
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What is an inconsistent system?
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What is an independent system?
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What is a linear inequality?
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What is a system of linear inequalities?
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Study Notes
Algebra 1 Unit 4 Concepts
- Intersection: Refers to the specific point where two lines cross or meet.
- Linear Equation: Represents a relationship where the graph forms a straight line, typically expressed in the form Ax + By = C.
- System: A collection of similar and related elements that are analyzed together to understand relationships.
Solutions and Systems of Linear Equations
- Solution of a Linear Equation: An ordered pair (x, y) that fulfills the conditions of all equations present in a system.
- Substitution Method: A technique for solving systems of linear equations; it involves substituting one variable with an expression derived from another equation before solving for the remaining variable.
- Gaussian Elimination: A systematic method for solving systems of linear functions, achieved through adding or manipulating equations to eliminate variables.
Types of Systems
- Coincide: When two lines share all points in common; such lines are termed coincident.
- Consistent System: A linear equation system that has at least one solution, indicating that the equations intersect at least at one point.
- Dependent System: Defines a system of linear equations that yields an infinite number of solutions, meaning the equations represent the same line.
- Inconsistent System: Characterizes a linear equation system that has no solution, implying the lines are parallel and never intersect.
- Independent System: An assortment of linear equations that has precisely one solution, indicating the lines intersect at a single point.
Inequalities
- Linear Inequality: A mathematical statement involving a linear expression that is not equal to another; can be represented with inequality symbols (e.g., Ax + By > C).
- System of Linear Inequalities: Consists of two or more linear inequalities evaluated together to determine the feasible region for solutions.
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Description
Test your knowledge of key concepts in Algebra 1, specifically focusing on Unit 4 vocabulary. This set of flashcards covers important terms such as intersection, linear equations, and solutions. Perfect for students looking to reinforce their understanding of algebraic concepts.