Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1
Solve each system by graphing. Tell whether the system has one solution,
infinitely many solutions, or no solution.


  1. y = x + 3 23. y = 2 x - l 24. 3x + y = 2
    y — x — 1 3y = 6x — 5 4y = 12 — 12x

  2. 2x-2y = 5 26. y=2x-2 27. y-x=5
    y = x — 4 2y=4x — 4 3y = 3x + 15

  3. 2x + 2y = 4 29. 2y = x - 2 30. 3x - y = 2
    12 - 3x = 3y 3y = | x — 3 4y = - x + 5


See Problem 3.

0 Apply @ 31. Think About a Plan You are looking for an after-school job. One job pays $9 p er
hour. A nother pays $12 p e r hour, b u t you m u st buy a uniform th at costs $39. After
how m any h ours of w ork w ould your n e t earnings from either job be th e sam e?


  • W hat equations can you write to m odel th e situation?

  • How will graphing th e equations help you solve th e problem?



  1. Error Analysis A stu d en t graphs th e system y = - x + 3 an d y = - 2 x - 1 as
    show n at the right. The s tu d en t concludes there is no solution. D escribe and
    correct the student's error.

  2. Reasoning Suppose you graph a system of linear equations an d th e intersection
    p o in t appears to be (3, 7). Can you be sure th a t th e ordered p air (3, 7) is the
    solution? W hat m u st you do to be sure?

  3. Cell Phone Plans A cell p h o n e provider offers a p lan th a t costs $40 p er m o n th plus
    $.20 p er text m essage sen t or received. A com parable p lan costs $60 p e r m o n th b u t
    offers u nlim ited text m essaging.
    a. How m any text m essages w ould you have to sen d or receive in o rder for the
    plans to cost th e sam e each m onth?
    b. If you send or receive an average of 50 text m essages each m onth, w hich plan
    w ould you choose? Why?


Without graphing, decide whether each system has one solution, infinitely
many solutions, or no solution. Justify your answer.
1

h'
\ 2

A
-2 2 >

y
o
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  1. y = x - 4
    y = x - 3
    36. x-y= ~
    2x — 2y = — 1
    37. y = 5x — 1
    lOx = 2y + 2
    38. 3x + 2y = 1
    4y = 6x + 2

  2. Banking The graph at th e right shows the balances in two bank
    accounts over time. Use th e graph to w rite a system of equations
    giving the a m o u n t in each account over time. Let t = th e tim e in
    weeks an d let b = the balance in dollars. If th e accounts continue to
    grow as shown, w hen will they have the sam e balance?

  3. Open-Ended One equation in a system is y = | x — 2.
    a. Write a second e q u a tio n so th a t the system has one solution.
    b. Write a second e quation so th at th e system has no solution.
    c. Write a second equation so th at th e system has infinitely
    many solutions.


1 2 3 4 5 6 7
Time, f (weeks)

368 Chapter 6 Systems of Equations and Inequalities

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