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Algebra 1 Unit 4 Flashcards
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Algebra 1 Unit 4 Flashcards

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Questions and Answers

What is the definition of intersection?

  • A group of similar and related elements considered together.
  • An equation whose graph is a straight line.
  • An ordered pair (x, y) that satisfies all the equations in the system.
  • The point that two lines have in common. (correct)
  • 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?

    <p>An ordered pair (x, y) that satisfies all the equations in the system.</p> Signup and view all the answers

    Substitution is a method of solving systems of linear equations by ______.

    <p>substituting an expression for a variable.</p> Signup and view all the answers

    What is Gaussian elimination?

    <p>A method of solving systems of linear functions by adding equations together.</p> Signup and view all the answers

    What does it mean for lines to coincide?

    <p>To occupy the same space at the same time.</p> Signup and view all the answers

    What is a consistent system?

    <p>A system of linear equations that has at least one solution.</p> Signup and view all the answers

    What is a dependent system?

    <p>A system of linear equations with an infinite number of solutions.</p> Signup and view all the answers

    What is an inconsistent system?

    <p>A system of linear equations that has no solution.</p> Signup and view all the answers

    What is an independent system?

    <p>A system of linear equations that has exactly one solution.</p> Signup and view all the answers

    What is a linear inequality?

    <p>A relation where the expression on one side does not equal the expression on the other side.</p> Signup and view all the answers

    What is a system of linear inequalities?

    <p>A set of two or more linear inequalities considered together.</p> Signup and view all the answers

    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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    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.

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