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?
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Systems of Linear Equations and Inequalities Chapter Problems
Solve by graphing
Classwork
1. y = -x – 7
4
y= x–7
3
1
2. y = - x + 2
4
1
y=- x+3
2
3. y = -3x – 5
y=x+3
4. y = -2x + 5
1
y= x–2
3
5. y = -4x + 7
y = -3x + 3
3
6. y = x – 3
4
3
y= x+2
4
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
3
2
1
-2+
11. y = - x – 4
y=
1
12. y = -2x – 2
y = -3x – 6
13. y = x – 2
y=x+2
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3
14. y = x + 1
4
1
y=- x–4
2
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
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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
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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)
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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
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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
4
y= x+6
5
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
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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
4
96. y = - x + 4
3
2
y = x + 10
3
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?
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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.
5
y≤ x–2
2
1
y≥ x+2
2
106.
1
y≤ x–1
4
y < 5x – 5
107.
1
y>- x–3
3
5
y≤ x+3
3
108.
y > 2x – 5
3x + 4y < 12
109.
x+y≥ -3
5x – y ≤ -3
Homework
110.
1
y< x+2
2
y > 3x – 3
111.
y ≥ -x + 5
y ≤ 3x – 4
112.
y< x
1
4
y ≤ -x + 4
113.
y > 2x +4
2x – y ≤ 4
114.
3x – y ≥ - 1
x + y ≤ -3
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Unit Review
Multiple Choice
Choose the correct answer for each question.
1. Solve the system:
x - y = -8
x + 3y = 12
a. (-5,3)
c.
(6,2)
b. (7,1)
d. (-3,5)
2. Solve the system:
-x +4y = 12
5x - 2y = -6
a. (-12,0)
c.
(0,3)
b. (8,5)
d. (4,4)
3. Solve the system:
-3x + y = -7
2x - 5y = 22
a. (0,-7)
c.
(1,-4)
b. (0,-4.5)
d. No solution
4. Solve the system:
3x + 2y = 8
2x +3y = 7
a. (3,-0.5)
c.
(2,1)
b. (4,-2)
d. No solution
5. Solve the system:
y = 6x - 1
y=x+4
a. (1,5)
c.
b. (1,6)
d. (4,11)
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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)
c.
b. (0,2)
(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
c.
Intersect at (4,2)
b. Intersect at (2,4)
d. One solution
9. What is true of the graphs of the two lines 3x + 4y = 2 and 9x + 12y = 6?
a. No solution
c.
Intersect at (0,0)
b. Intersect at (0,.5)
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
c.
Intersect at (2,-5)
b. Intersect at (-3,0)
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
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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
c.
-3
b. 2
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
c.
3
b. 2
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
girls?
a. 60
c.
100
b. 80
d. 110
16. Which graph represents the following system of inequalities?
-x + y < - 1
2x + y ≥ 2
a.
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c.
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17. Which of these points is a solution of the system y >- 2x + 3 and -x + y > 0?
a. (2,-6)
c.
(5,2)
b. (-1,-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 l em e n t a r y s c h o o l s t u d e n t s a r e p u t t i n g o n a
p l a y a s a f u n d r a i s er . T h e s t u d e n t t i c k e t s c os t $ 2 . 0 0
e a c h a n d t h e a d u l t t i c k et s c o s t $ 4 e ac h . T he y s o l d
5 t im e s as m a n y s t u d e n t t i c k e ts a s a d u l t t i c k e t s .
They made $140. How many student and adult
t i c k e ts w e r e s o l d ?
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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.
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1.
2.
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50.
51.
52.
x=0, y=-7
x=4, y=1
x=-2, y=1
x=3, y=-1
x=4, y=-9
No solution
x=2, y=-2
x=-3, y=-2
x=-4, y=-1
x=-1, y=3
x=-5, y=3.5
x=-4, y=6
No solution
x=-4, y=-2
x=3, y=-1
x=-2, y=-4
x=-1, y=-1
x=4, y=2
x=3, y=2
x=-3, y=-3
x=7, y=4
x=8, y=4
x=-5, y=8
x=-9, y=6
x=-7, y=0
x=-8, y=6
No solution
x=-2, y=2
x=-4, y=1
x=-5, y=7
x=8, y=1
Same function
x=-3, y=-9
x=7, y=2
x=5, y=6
x=2, y=7
x=8, y=5
no solution
x=2, y=0
x=3, y= -5
x=10, y=6
x=9, y=8
x=-9, y=5
x=-10, y=8
x=6, y=-5
No solution
x=4, y=0
x=10, y=-3
x=1, y=7
x=8, y=0
x=0, y=2
x=7, y=6
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Answer Key
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
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105.
106.
107.
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108.
109.
110.
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111.
112.
113.
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(Parallel Lines)
114.
Review Answers
1.
2.
3.
4.
5.
6.
7.
22.
D
C
C
C
A
B
C
y>-x
y≥
−1
2
8.
9.
10.
11.
12.
13.
14.
D
D
A
A
C
A
D
15.
16.
17.
18.
19.
C
A
D
D
Answers
vary
20. Answers
vary
21. 10 adults
and 50
students
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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