Math Practice 101
Homework Explained - Math Practice 101

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Grade 8 HMH Go Math - Answer Keys
Chapter 8:Solving Systems of Linear Equations; Lesson 5: Solving Solving Special Systems


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Guided Practice

Use the graph to solve each system of linear equations

  • Question 1 (request help)

    A. \(\begin{cases}
        4x - 2y = -6\\
        2x - y = 4
        \end{cases}\)

    B.\(\begin{cases}
        4x - 2y = -6\\
        x + y = 6
        \end{cases}\)

    C.\(\begin{cases}
          2x - y = 4\\
         6x - 3 y = 12
        \end{cases}\)
    STEP 1 Decide if the graphs of the equations in each system intersect, are parallel, or are the same line.
  • System A: The graphs    
    System B: The graphs   
    System C: The graphs   
  • Question 1 (request help)

    STEP 2 Decide how many points the graphs have in common.

    a. Intersecting lines have  _______________ point(s) in common.

    b. Parallel lines have _______________ point(s) in common.

    c. The same lines have___________ point(s) in common.
  • a.    
    b.   
    c.    
  • Question 1 (request help)

    STEP 3 Solve each system.

    System A has __________ points in common, so it has __________ solution.

    System B has __________ point in common. That point is the solution, __________.

    System C has __________ points in common. ________ ordered pairs on the line will make both equations true.
  • Type below:

Solve each system. Tell how many solutions each system has. 

  • Question 2 (request help)

    \(\begin{cases}
    x - 3y = 4\\
    -5x + 15 y = - 20
    \end{cases}\)
  •    
  • Question 3 (request help)

    \(\begin{cases}
    6x + 2y = -4\\
    3x + y = 4
    \end{cases}\)
  •    
  • Question 4 (request help)

    \(\begin{cases}
    6x - 2y = -10\\
    3x + 4y = -25
    \end{cases}\)
  •    

ESSENTIAL QUESTION CHECK-IN

  • Question 5 (request help)

    When you solve a system of equations algebraically, how can you tell whether the system has zero, one, or an infinite number of solutions?
  • Type below:

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