Homework Explained - Math Practice 101

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Grade 8 HMH Go Math - Answer Keys
Chapter 8:Solving Systems of Linear Equations; Lesson 4: Solving Systems by Elimination with Multiplication


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  • Question 10 (request help)

    Explain the Error Gwen used elimination with multiplication to solve the system

     \(\begin{cases}
    2x + 6y = 3\\
    x - 3y = -1
    \end{cases}\)

     Her work to find \(x\) is shown. Explain her error. Then solve the system.

    \(\begin{align}
    2(x - 3y)& = -1\\
    2x - 6y& = -1\\
    +2x + 6y& = 3\\
    \hline
    4x + 0y&= 2\\
    x& =\frac{1}{2}
    \end{align}\)

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  • Question 11 (request help)

    Represent Real-World Problems At Raging River Sports, polyester-fill sleeping bags sell for $79. Down-fill sleeping bags sell for $149. In one week  the store sold 14 sleeping bags for $1,456.
    a. Let \(x\) represent the number of polyester-fill bags sold and let \(y\) represent the number of down-fill bags sold. Write a system of equations you can solve to find the number of each type sold.

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  • Question 11 (request help)

    b. Explain how you can solve the system for \(y\) by multiplying and subtracting.

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  • Question 11 (request help)

    c. Explain how you can solve the system for \(y\) using substitution.

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  • Question 11 (request help)

    d. How many of each type of bag were sold?

  •    polyester-fill
       down-fill
  • Question 12 (request help)

    Twice a number plus twice a second number is 310. The difference between the numbers is 55. Find the numbers by writing and solving a system of equations. Explain how you solved the system.

  • \(x=\)   
    \(y=\)   

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