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Systems of Linear Equations and Inequalities Chapter Questions

1. What are the different ways to solve a system of linear equations?

2. When do you get an answer to a system of linear equations that has one solution, no solution and

infinitely many solutions?

3. How is a system of inequalities graphed?


Systems of Linear Equations and Inequalities Chapter Problems

Solve by graphing

Classwork

1. y = -x – 7

y = 4

3x – 7

2. y = - 1

4x + 2

y = - 1

2x + 3

3. y = -3x – 5

y = x + 3

4. y = -2x + 5

y = 1

3x – 2

5. y = -4x + 7

y = -3x + 3

6. y = 3

4x – 3

y = 3

4x + 2

7. 3x + 2y = 2

x + 2y = -2

8. x + 3y = -9

2x – y = -4

9. x – 2y = 2

x + 4y = -8

10. 5x + y = -2

x + y = 2

Homework

11. y = - 3

2x – 4

y = - 1

2 + 1

12. y = -2x – 2

y = -3x – 6

13. y = x – 2

y = x + 2


14. y = 3

4x + 1

y = - 1

2x – 4

15. y = x – 4

y = -x + 2

16. x + y = 2

4x – y = -4

17. 4x – y = -3

x + y = -2

18. x + 2y = 8

x – y = 2

19. x – 3y = -3

2x + 3y = 12

20. 2x – 3y = 3

x + 3y = -12

Solve by Substitution

Classwork

21. x = 4y – 9

x = y + 3

22. 5x = -2y + 48

x = -3y + 20

23. y – 4x = 28

y = -2x – 2

24. y + 2x = -12

y = x + 15

25. x = -2y – 7

2x + y = -14

26. x = 5y – 38

x = -4y + 16

27. y = 2x + 3

4x – 2y = 8

28. 4x + y = -6

-6x + 2y = 16

29. 6x – 2y = 8

-3x + y = -4


30. -2x + 7y = 15

-3x – 8y = 4

Homework

31. y = -5x + 41

-2x = -14 – 2y

32. y = 3x + 6

-6x + 2y = 12

33. y – 3x = 0

y = -3x – 18

34. x = -3y + 13

4x – 4y = 20

35. x = -4y + 29

5x + 2y = 37

36. y = -2x + 11

5y – 2x = 31

37. 5y – 5x = -15

y = -3x + 29

38. -2x + 4y = 1

x – 2y = -1

39. -6x + y = -12

5x + 4y = 10

40. -2x – 3y = 9

-x – y = 2

Solve by Elimination (Addition & Subtraction)

Classwork

41. 3x + y = 36

5x + y = 56

42. x + 2y = 25

x + 3y = 33

43. 3x – 5y = -52

x – 5y = -34

44. 2x + 3y = 4

-2x + 5y = 60


45. 2x + 2y = 2

5x – 2y = 40

46. -x + 2y = 14

x – 2y = -11

47. 4x – y = 16

4x + 2y = 16

48. 2x + 5y = 5

-2x + y = -23

49. 2x – 2y = -12

x – 2y = -13

50. 5x + 5y = 40

-5x + 3y = -40

Homework

51. 4x – y = -2

4x + 5y = 10

52. 2x + 4y = 10

-4x + 4y = 52

53. -3x – 5y = 49

3x + 4y = -44

54. -4x + 3y = 39

5x – 3y = -45

55. -5x – 2y = -5

-x – 2y = -1

56. x + 5y = -4

-x + 2y = -10

57. -4x + 2y = -44

4x + 4y = 20

58. x + 2y = 4

x + 5y = -2

59. 3x – y = -5

-3x – 2y = -10

60. 3x – y = 11

-3x – 5y = -71

Solve by Elimination (Multiply First)


Classwork

61. 5x – 4y = 47

-x – 16y = 125

62. 3x – 2y = 33

-4x – 4y = 16

63. 2x + y = 21

4x + 3y = 51

64. -3x + 3y = -27

12x + 5y = 108

65. 3x + 4y = 3

-12x – y = -57

66. 2x + 5y = -7

8x + 3y = 57

67. 4x + 3y = 33

8x + y = 31

68. -7x – 5y = 21

-10x – 8y = 24

69. 16x + 16y = -16

-12x – 12y = 12

70. -6x – 10y = 22

10x – 3y = -17

Solve by Elimination (Multiply First)

Homework

71. –x + y = -5

-3x + 4y = -12

72. -2x – y = 2

-6x + 3y = -18

73. -2x + 2y = 16

6x – y = -13

74. -4x – 5y = -9

3x + 10y = 13

75. 3x – 2y = -26

6x – 4y = -70


76. x + 5y = -12

3x + y = 6

77. x + y = 14

4x – 2y = 2

78. -50x + 50y = 0

20x – 20y = -20

79. 7x – 4y = -18

-4x + 3y = 11

80. 3x + 4y = -4

2x – 7y = 7

Choose Your Own Strategy

Classwork

81. –x + 4y = 5

x + 4y = 11

82. 3x – y = 7

4x – 2y = 8

83. 2y + 5x = 35

y = 4x – 28

84. 5x – 4y = -39

-3x – 4y = -15

85. y = -5x + 59

4x + y = 49

86. y = x + 6

y = 4

5x + 6

87. -2x + 4y = 28

2x – 3y = -18

88. y = -x + 12

3y + 3x = 36

89. 2x + 4y = -10

-4x – 12y = 36

90. –x – 5y = -3

-2x + 5y = 9


Choose Your Own Strategy

Homework

91. -3x + 5y = -39

12x – 4y = 60

92. y = 3x – 18

y – 3x = -24

93. x + 3y = 16

-x + 4y = 5

94. x = -3y – 19

x + 5y = -22

95. 3x – 3y = 12

9x + 2y = 102

96. y = - 4

3x + 4

y = 2

3x + 10

97. 3x + 2y = 21

-3x + 5y = 21

98. –x – y = 7

-x + 5y = 19

99. 4x + y = -28

-2x + 2y = 24

100. x = 2y – 7

-x + 4y = 17

Writing Systems to Model Situations

Classwork

101. The admission fee at a carnival is $3.00 for children and $5.00 for adults. On the first day 1,500

people enter the fair and $5740 is collected. How many children and how many adults attended the

carnival?

102. A builder placed two orders with the hardware store. The first order was for 25 sheets of plywood

and 4 boxes of nails and the bill totaled $357. The second order was for 35 sheets of plywood and 2

boxes of nails and the bill totaled $471. The bills do not list the per-item price. What were the prices of

one piece of plywood and one box of nails?


Homework

103. Two friends bought some markers and pens. The first bought 4 markers and 5 pens and it cost

him $6.71. The second friend bought 5 markers and 3 pens, which cost her $7.12. What is the price

for one marker and one pen?

104. The ticket price for the movies is $7.50 for children and $10.50 for adults. One night 825 people

bought tickets and $8005.50 was collected from ticket sales. How many children and how many

adults bought tickets.

Solving Systems of Inequalities by Graphing

Classwork

105. y ≤ 5

2x – 2

y ≥ 1

2x + 2

106. y ≤ 1

4x – 1

y < 5x – 5

107. y > - 1

3x – 3

y ≤ 5

3x + 3

108. y > 2x – 5

3x + 4y < 12

109. x + y ≥ - 3

5x – y ≤ -3

Homework

110. y < 1

2x + 2

y > 3x – 3

111. y ≥ -x + 5

y ≤ 3x – 4

112. y < 1

4x

y ≤ -x + 4

113. y > 2x +4

2x – y ≤ 4

114. 3x – y ≥ - 1

x + y ≤ -3


Unit Review

Multiple Choice

Choose the correct answer for each question.

1. Solve the system:

x - y = -8

x + 3y = 12

a. (-5,3)

b. (7,1)

c. (6,2)

d. (-3,5)


-x +4y = 12

5x - 2y = -6

a. (-12,0)

b. (8,5)

c. (0,3)

d. (4,4)


-3x + y = -7

2x - 5y = 22

a. (0,-7)

b. (0,-4.5)

c. (1,-4)

d. No solution


3x + 2y = 8

2x +3y = 7

a. (3,-0.5)

b. (4,-2)

c. (2,1)

d. No solution


y = 6x - 1

y = x + 4

a. (1,5)

b. (1,6)

c. (2,5)

d. (4,11)


6. If the graph of a system shows two parallel lines, then

a. there are infinite solutions

b. there is no solution

c. there may be a solution if the lines are extended

d. something is incorrect with the graph

7. What point is the intersection of the graphs of the lines 3x + y = 6 and

-3x + y = -6?

a. (2,1)

b. (0,2)

c. (2, 0)

d. (3, 3

8. What is true of the graphs of the two lines x = 2y - 6 and x = -3y – 14?

a. No solution

b. Intersect at (2,4)

c. Intersect at (4,2)

d. One solution

9. What is true of the graphs of the two lines 3x + 4y = 2 and 9x + 12y = 6?

a. No solution

b. Intersect at (0,.5)

c. Intersect at (0,0)

d. Infinitely many solutions

10. What is true of the graphs of the two lines 3x + 5y = -9 and -6x - 10y = -12?

a. No solution

b. Intersect at (-3,0)

c. Intersect at (2,-5)

d. Infinitely many solutions

11. To solve 4x + 2y = 10 and x + y = 4 by elimination,

a. first multiply the second equation by -2

b. first multiply the second equation by -1

c. first multiply the second equation by 2

d. first multiply the second equation by 4


12. Bob wants to sub 3x + y = 13 into 4x + 3y = 6, he needs to

a. convert the equation to 3x = 13 – y

b. convert the equation x=13-y

c. convert the equation to y= 13 – 3x

d. convert the equation to x = -y-13

13. What is the value of y in the following system of equations?

x + 5y = 7

x - 3y = –1

a. 1

b. 2

c. -3

d. 4

14. What is the value of the y-coordinate of the solution to the

system of equations - 3 x + y = 9 and x − y = 7?

a. 6

b. 2

c. 3

d. -15

15. F i v e times as many girls as boys went to the dance. If a

total of 120 students went to the dance, how many were

g ir ls?

a. 60

b. 80

c. 100

d. 110

16. Which graph represents the following system of inequalities?

-x + y < - 1

2x + y ≥ 2

a. b. c.


17. Which of these points is a solution of the system y >- 2x + 3 and -x + y > 0?

a. (2,-6)

b. (-1,-2)

c. (5,2)

d. (1,3)

18. Which coordinate point is in the solution set for the system of inequalities shown in the

accompanying graph?

a. (1,3)

b. (-1,3)

c. (1,–5)

d. (-3,0)

Short Constructed Response – Write the correct answer for each question.

19. Sketch a graph of a system that has infinitely many solutions.

20. Sketch a graph of a system that has no solution

.

21. The e lementary school s tudents are put t ing on a

p lay as a fundraiser . The s tudent t ickets cost $2.00

each and the adul t t ickets cost $4 each. They sold

5 t imes as many s tudent t ickets as adul t t ickets .

They made $140. How many s tudent and adul t

t ickets were sold?


22. Write the system of inequalities graphed below

Extended Constructed Response - Solve the problem, showing all work.

23. Telephone company A charges $20 per month and $0.10 per text. Telephone company B charges

$15 per month and $0.20 per text. Let t = the number of texts and C = cost.

e. Write an equation to represent the cost of each plan.

f. Solve the system by graphing.

g. Explain what the solution to the system means in terms of what telephone company to

provide services.


Answer Key

1. x=0, y=-7 2. x=4, y=1 3. x=-2, y=1 4. x=3, y=-1 5. x=4, y=-9 6. No solution 7. x=2, y=-2 8. x=-3, y=-2 9. x=-4, y=-1 10. x=-1, y=3 11. x=-5, y=3.5 12. x=-4, y=6 13. No solution 14. x=-4, y=-2 15. x=3, y=-1 16. x=-2, y=-4 17. x=-1, y=-1 18. x=4, y=2 19. x=3, y=2 20. x=-3, y=-3 21. x=7, y=4 22. x=8, y=4 23. x=-5, y=8 24. x=-9, y=6 25. x=-7, y=0 26. x=-8, y=6 27. No solution 28. x=-2, y=2 29. x=-4, y=1 30. x=-5, y=7 31. x=8, y=1 32. Same function 33. x=-3, y=-9 34. x=7, y=2 35. x=5, y=6 36. x=2, y=7 37. x=8, y=5 38. no solution 39. x=2, y=0 40. x=3, y= -5 41. x=10, y=6 42. x=9, y=8 43. x=-9, y=5 44. x=-10, y=8 45. x=6, y=-5 46. No solution 47. x=4, y=0 48. x=10, y=-3 49. x=1, y=7 50. x=8, y=0 51. x=0, y=2 52. x=7, y=6

53. x=8, y=-5 54. x=-6, y=5 55. x=1, y=0 56. x=6, y=-2 57. x=9, y=-4 58. x=8, y=-2 59. x=0, y=5 60. x=7, y=10 61. x=3, y=-8 62. x=5, y=-9 63. x=6, y=9 64. x=9, y=0 65. x=5, y=-3 66. x=9, y=-5 67. x=3, y=7 68. x=-8, y=7 69. infinite solutions 70. x=-2, y=-1 71. x=8, y=3 72. x=1, y=-4 73. x=-1, y=7 74. x=1, y=1 75. No solution 76. x=3, y=-3 77. x=5, y=9 78. no solution 79. x=-2, y=1 80. x=0, y=-1 81. x=3, y=2 82. x=3, y=2 83. x=7, y=0 84. x=-3, y=6 85. x=10, y=9 86. x=0, y=6 87. x=6, y=10 88. x=0, y=12 89. x=3, y=-4 90. x=-2, y=1 91. x=3, y=-6 92. No solution 93. x=7, y=3 94. x=-14.5, y=-1.5 95. x=10, y=6 96. x=-3, y=8 97. x=3, y=6 98. x=-9, y=2 99. x=-8, y=4 100. x=3, y=5 101. Adults: 620, Children: 880 102. Plywood: $13, Box of nails: $8 103. Pen: $0.39, Marker: $1.19 104. Children: 219, Adults 606


105.

106.

107.


108.

109.

110.


111.

112.

113.


(Parallel Lines)

114.

Review Answers

1. D

2. C

3. C

4. C

5. A

6. B

7. C

8. D

9. D

10. A

11. A

12. C

13. A

14. D

15. C

16. A

17. D

18. D

19. Answers

vary

20. Answers

vary

21. 10 adults

and 50

students

22. y>-x

y≥ −1

2 x – 6

23.

a. C = .10t + 20

C = .20t + 15

b. 𝐶 = .10𝑡 + 20

𝑐. The plans cost the same with 50 text messages.

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