Solve each system by graphing. Tell whether the system has one solution,
infinitely many solutions, or no solution.- y = x + 3 23. y = 2 x - l 24. 3x + y = 2
y — x — 1 3y = 6x — 5 4y = 12 — 12x - 2x-2y = 5 26. y=2x-2 27. y-x=5
y = x — 4 2y=4x — 4 3y = 3x + 15 - 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?
- 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. - 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? - 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.
1h'
\ 2A
-2 2 >y
o
\
\t ^- 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 - 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? - 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