Solving Linear Systems by Elimination
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Questions and Answers

Complete the second equation below so that the terms in the system align: 2y = 3x - ____.

-22

Which equation results when you add the equations?

  • 8y = -20
  • 8y = -40 (correct)
  • 8y = -50
  • 8y = -30

    • What is the solution to the system?

    (4, -5)

    Which of the following shows the system with like terms aligned?

    <p>Both A and B</p> Signup and view all the answers

    How can subtracting the equations help you solve the system?

    <p>It eliminates the y-terms.</p> Signup and view all the answers

    What is the solution to the system?

    <p>(0.5, 3)</p> Signup and view all the answers

    You could produce a pair of like terms with opposite coefficients by multiplying the first equation by what number?

    <p>6</p> Signup and view all the answers

    To solve the system by elimination, __________ the equations.

    <p>add</p> Signup and view all the answers

    What is the solution to the system?

    <p>(-2, -4)</p> Signup and view all the answers

    How could you solve this system using elimination? Check all that apply.

    <p>Multiply the first equation by 5 and the second equation by 2, then add.</p> Signup and view all the answers

    How many solutions does the system have?

    <p>Exactly one</p> Signup and view all the answers

    What is the solution to the system?

    <p>(0, -3)</p> Signup and view all the answers

    It takes the printer ________ min to print a black-and-white page and ________ min to print a color page.

    <p>1/12, 1/8</p> Signup and view all the answers

    Explain how knowing how to find the least common multiple (LCM) can help in solving the system of equations.

    <p>The LCM of 6 and 8 is 24. Knowing this, multiply the first equation by 4 and the second by -3 to get opposite coefficients, then add the equations to eliminate x.</p> Signup and view all the answers

    Study Notes

    Solving Linear Systems by Elimination

    • The system of equations includes 3x + 6y = -18 and 2y = 3x - 22.
    • Completing the second equation results in aligning terms with -3, 2, -22.

    Adding Equations

    • Adding equations in a system can yield a new equation; for instance, the result can be 8y = -40.

    Solutions to Systems

    • One solution to a system can be (4, -5), another is (0.5, 3), and yet another is (-2, -4).
    • A specific solution is also (0, -3).

    Aligning Like Terms

    • Aligning like terms in a system can result in equations such as -4x + 0.4y = -0.8 and 6x + 0.4y = 4.2.

    Subtracting Equations

    • Subtracting equations can eliminate terms, such as y-terms, making it easier to find solutions.

    Multiplication for Elimination

    • To create oppositional coefficients, multiply the first equation of a system by 6 to produce like terms with 1/2x + 3/2y = -7 and -3x + 2y = -2.
    • If multiplied correctly, resulting equations for elimination may look like 3x + 9y = -42 and -3x + 2y = -2.

    Solving Through Elimination

    • You can solve by multiplying the first equation by 5 and the second by 2, or by multiplying the first by 2 and the second by 5 and then subtracting.

    System Solutions

    • Systems can consistently have one solution, or multiple solutions may be possible based on the equations given.

    Application of the Problem

    • Given the printer scenario, the system is defined as 24b + 4c = 2 1/2 and 30b + 6c = 3 1/4.
    • The solution to the system reveals the time taken to print, where a black-and-white page takes 1/12 minutes and a color page takes 1/8 minutes.

    Least Common Multiple (LCM)

    • The LCM helps in determining the right multiplication to eliminate variables, as with the system 6x - 2y = 28 and 8x + 3y = 14.
    • For elimination in the provided example, the LCM of 6 and 8 is 24, enabling multiplication of the first equation by 4 and the second by -3.

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    Description

    Test your understanding of solving linear systems using the elimination method with these flashcards. This quiz will challenge you to align terms, derive sums, and find solutions for a given system of equations.

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