Algebra 1 Common Core Student Edition, Grade 8-9

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Tell whether the system has one solution, infinitely many solutions, or

no solution.

See Problem 4.

26. y = |x + 3
    2 y — x = 6


27. 5 = | x + 3y
    10 — x = 6y
    27. 6y = - 5 x + 24
    2.5x + 3y = 12


28. 17 = lly + 12jc
    12x + l l y = 14


29. x = - 7 y + 34
    x + 7y = 32


30. 1.5 x + 2y = 11
    3x + 6y = 22

w

32. Geom etry The rectangle show n has a p erim e te r of 34 cm an d th e given area.
    Its length is 5 m ore th a n twice its w idth. W rite an d solve a system of equations
    to find th e dim ensions of th e rectangle.


33. W riting W hat w ould your first step b e in solving th e system below? Explain.
    1.2x + y = 2
    1.4y = 2.8x + 1


34. Coins You have $3.70 in dim es a n d q uarters. You have 5 m ore quarters th a n dimes.
    How m any of each type of coin do you have?
    3 5. E rro r A n alysis D escribe a n d correct th e error at th e right in
    finding th e solution of th e following system:
    7x + 5y = 14
    x + 8y = 21


35. Art An artist is going to sell two sizes of prints at a n art fair.
    The artist will charge $20 for a sm all p rin t a n d $45 for a large
    print. The artist w ould like to sell twice as m any sm all prints
    as large prints. The b o oth th e artist is renting for th e day
    costs $510. How m any of each size p rin t m u st the artist sell
    in order to break even at th e fair?

A = 52 cm 2

Step 2

x + 8 y = 21

x = 2 4 " - 8 y

x + .8 fY 21

8y = 21

21

Th^sfstem has infinitefyrriany

utions.

(21

37. Think About a Plan At a certain high school, 350 stu d en ts are taking an algebra
    course. The ratio of boys to girls taking algebra is 33 : 37. H ow m any m ore girls are
    taking algebra th a n boys?
    
    
    • How can you w rite a system of equations to m o d el th e situation?
    
    
    • W hich equ atio n will you solve for a variable in th e first step of solving the
      system? Why?
    
    
    • How can you in terp ret th e solution in th e context of th e problem?
    
    
    
    


38. a. Compare and Contrast Using a graph, how can you tell w h en a system of linear
    equations h as no solution?
    b. Using substitution, how can you tell w h en a system of linear
    equations has n o solution?
    c. How can you tell by looking at a table of values if two lines will
    intersect in one point, no points, or an infinite num ber of points?


39. Fireworks A pyrotechnician plans for two fireworks to
    explode together at th e sam e height in th e air. They travel
    at speeds show n at th e right. Firework B is lau n ch e d 0.25
    s before Firework A. How m any seconds after Firework B
    launches will b o th fireworks explode?

376 Chapter 6 Systems of Linear Equations and Inequalities