Algebra 1 Common Core Student Edition, Grade 8-9

Mid-Chapter Quiz

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Do yo u k n o w H OW?

Solve each system by graphing. Tell whether the
system has one solution, infinitely m any solutions,^
or no solution.

1. y = x - 1

y = —3x - 5

2. y = | x — 2
   3y - 4x = -6


3. y = 3x - 4
   y — 3x = 1


4. y = 3x - 14
   y - x = 10

Solve each system using substitution.

5. y = 2x + 5
   y = 6x + 1


6. x = y + 7
   y — 8 = 2x


7. 4x + y = 2
   3y + 2x = — 1


8. 4x + 9y = 24
   y = ~\x + 2

Solve each system using elimination.

9. 2x + 5y = 2
   3x — 5y = 53


10. 4x + 2y = 34
    lOx — 4y = —5


11. l l x 13y = 89
    -llx + 13y= 107

Write and solve a system of equations to solve each

problem. Explain why you chose the method you used.

13. G eom etry The length of a rectangle is 3 tim es
    th e w idth. The p erim e te r is 44 cm. W hat are the
    d im en sio n s of th e rectangle?


14. Farming A f a r m e r grow s o n ly p u m p k i n s a n d c o r n
    on h e r 420-acre farm. This year she w ants to p lant
    250 m ore acres of corn th a n pum pkins. How m any
    acres of each crop should th e farm er plant?


15. Coins You have a total of 21 coins, all nickels an d
    dim es. The total value is $1.70. How m any nickels
    an d how m any dim es do you have?


16. Business Suppose you start a n ice cream business.
    You buy a freezer for $200. It costs you $.45 to m ake
    each single-scoop ice cream cone. You sell each cone
    for $1.25. How m an y cones do you n ee d to sell to
    break even?

Do y o u UN DERSTAND?

@ Reasoning Without solving, tell which method

you would choose to solve each system: graphing,

substitution, or elimination. Explain your answer.

17. y = 2x — 5
    4y + 8x = 15


18. 2y+7x=3
    y - 7x = 9


19. Reasoning If a system of linear equations has
    infinitely m any solutions, w h at do you know
    about the slopes and y-intercepts of the graphs
    of the equations?
    @20. Open-Ended W rite a system of eq u atio n s th at you
    w ould solve using substitution.


20. Reasoning Suppose you write a system of equations
    to find a break-even p o in t for a business. You solve
    th e system a n d find th a t it has no solution. W hat
    w ould th a t m e a n in term s of th e business?


21. 3x + 6y = 42

• 7 x + 8y = -1 0 9

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Ch ap t er 6 M id - Chap t er Qu iz^393