Algebra 2: Systems of Equations Flashcards
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Questions and Answers

Which of the following statements would describe solving a system of equations with 6 variables?

  • Solving a 3 order system
  • Solving a 6 order system (correct)
  • Solving an order system
  • Solving a system

Determine if the solution set for the system of equations shown is the empty set, contains one point, or is infinite: x + y = 4, x - y = 0.

  • {}
  • 1 solution (correct)
  • infinite

Determine if the solution set for the system of equations shown is the empty set, contains one point, or is infinite: x - y = 5, 2x + y = 1.

  • {}
  • infinite
  • 1 solution (correct)

Determine if the solution set for the system of equations shown is the empty set, contains one point, or is infinite: x + y = 5, x + y = 7.

<p>{} (C)</p> Signup and view all the answers

Determine if the solution set for the system of equations shown is the empty set, contains one point, or is infinite: 3x + 2y = 6, x - y = 2.

<p>1 solution (A)</p> Signup and view all the answers

Determine if the solution set for the system of equations shown is the empty set, contains one point, or is infinite: 2x - y = 7, 2y = 4x - 14.

<p>infinite (C)</p> Signup and view all the answers

Which of the following points is a solution to the system of equations shown: 4x + y = 1, y = x + 6?

<p>(-1, 5) (B)</p> Signup and view all the answers

Which of the following points is a solution to the system of equations shown: y - x = -1, x + y = -5?

<p>(-2, -3) (A)</p> Signup and view all the answers

Study Notes

Solving Systems of Equations

  • 6 Order System: The correct terminology for addressing a system comprising six variables is "Solving a 6 order system."
  • Solution Set Types:
    • Systems can lead to three types of solution sets: empty set, one solution, or infinite solutions.

Specific Systems and Their Solutions

  • Equations x + y = 4 and x - y = 0: This system has one solution.
  • Equations x - y = 5 and 2x + y = 1: This system also results in one solution.
  • Equations x + y = 5 and x + y = 7: These equations contradict each other, leading to an empty set of solutions.
  • Equations 3x + 2y = 6 and x - y = 2: This system yields one solution.

Infinite Solutions

  • Equations 2x - y = 7 and 2y = 4x - 14: Represent a scenario with infinite solutions, indicating dependent equations.

Identifying Solutions from Given Points

  • System of Equations (4x + y = 1, y = x + 6): The point (-1, 5) satisfies this system.
  • System of Equations (y - x = -1, x + y = -5): The point (-2, -3) is a valid solution.

Summary

  • Understanding how to classify solutions is crucial for analyzing systems of equations.
  • Identifying solutions from proposed points requires substitution into the equations.

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Test your understanding of solving systems of equations with multiple variables through these flashcards. Each card presents a statement or a question related to the topic, helping you grasp the concepts better. Perfect for Algebra 2 students looking to reinforce their skills.

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