Algebra 1 Common Core Student Edition, Grade 8-9

Lesso n Ch eck

Do y o u k n o w H OW?

Solve each system by graphing.

1. y = x + 7 2. y = | x + 6
   y = 2x + 1


2. y = - 3 x - 3
   y = 2x + 2

y = x — 2

4. y= - x - 4
   4 x - y = - 1


5. C o n ce rt T ickets Tickets for a concert cost $10 each
   if you order th em online, b u t you m u st pay a service
   charge of $8 p er order. The tickets are $12 each if you
   buy th em at th e door on th e night of th e concert.
   a. Write a system of eq u atio n s to m odel the
   situation. Let c be th e total cost. Let t be the
   n u m b er of tickets.
   b. G raph the equations an d find the intersection
   point. W hat does this po in t represent?

Do y o u UN DERSTAN D? ^ P R A O i a s

6. V o c a b u l a r y M atch each type of system w ith the

n u m b e r of solutions th e system has.

A. inconsistent I. exactly one

B. consistent a n d d e p e n d e n t II. infinitely many

C. consistent a n d in d e p e n d e n t III. no solution

7. W riting S uppose you graph a system of linear
   equations. If a p o in t is on only one of th e lines, is it a
   solution of th e system? Explain.


8. R e a s o n i n g Can a system of two linear equations
   have exactly two solutions? Explain.


9. Reasoning Suppose you find th at two linear
   eq u atio n s are tru e w h e n x = - 2 an d y = 3. What
   can you conclude ab o u t th e graphs of the equations?
   Explain.

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

Practice

MATHEMATICAL

PRACTICES

Solve each system by graphing. Check your solution.

10. y = 2x
    y = — 2x + 8


11. y = x — 4
    y= -x

See Problem 1.

16. y = ^x + 2
    I2
    y=?

i

v

kx + 6

1 -7

y~2x^12. y = | x +^1

y = |x + 3 y = —3x +11

y = -x + 3 15. 4x —y = - 1

y = x + 1 —x + y = x —

2 x - y = —5 18. x= -3

1 CMx 1 II 1 i-H II

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19. Student Statistics The n u m b e r of rig h t-h an d e d stu d en ts in a m athem atics class See Problem 2.
    is nine tim es th e n u m b e r of left-handed students. The total n u m b e r of students
    in the class is 30. How m any rig h t-h an d e d stu d en ts are in the class? How m any
    left-handed stu d en ts are in th e class?


20. Plants A p la n t nursery is growing a tree th a t is 3 ft tall a n d grows at an average rate
    of 1 ft p e r year. A nother tree at th e nursery is 4 ft tall an d grows at an average rate of
    0.5 ft p er year. After how m any years will th e trees b e th e sam e height?


21. Fitness At a local fitness center, m em b ers pay a $20 m em b ersh ip fee an d $3 for
    each aerobics class. N onm em bers pay $5 for each aerobics class. For w h at n u m b er
    of aerobics classes will th e cost for m em b ers a n d n o n m e m b e rs b e th e sam e?

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