Systems of Linear Equations
Solve by graphing
Class Work
1. y = -x – 7
4
3
y= x–7
1
2. y = - 4x + 2
1
y = - 2x + 3
3. y = -3x – 5
y=x+3
4. y = -2x + 5
1
3
y= x–2
5. y = -4x + 7
y = -3x + 3
3
6. y = 4x – 3
3
4
y= x+2
4
7. y = 3x + 3
2
y = - 3x – 3
1
8. y = 3x + 2
y = -x – 2
9. y = 4x – 1
y = -x + 4
10. y = 3x – 4
y = 4x + 10
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
3
4
14. y = x + 1
1
y = - 2x – 4
15. y = x – 4
y = -x + 2
16. y = -4x – 1
y = x – 11
17. y = -3x – 3
1
2
y= x+4
2
18. y = - 5x + 3
2
y = 5x – 1
19. y = -x – 2
1
2
y=- x+2
20. y = x + 5
y = -x + 3
Solve by Substitution
Class Work
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. x = -4y + 8
x = 3y + 8
29. 5y + 5x = 85
y = 4x – 18
30. x = y – 12
x = 5y – 40
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. -4x = 3y + 32
x = -5y – 8
39. y = -3x – 1
-4y + x = -9
40. y = -4x + 17
-3y – x = -7
Solve by Elimination (Addition & Subtraction)
Class Work
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)
Class Work
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. 3x + 3y = 31
-9x – 5y = -67
69. –x – y = -8
-4x + 2y = 22
70. 2x + y = 0
-8x + 4y = 80
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. -3x + 3y = -3
-12x + 5y = -61
79. 3x + 2y = 27
-9x + 4y = -51
80. 4x + 4y = 20
2x – 16y = -44
Choose Your Own Strategy
Class Work
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 = 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
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
3
96. y = - x + 4
2
y = 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
Class Work
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?
103. The student council is running a contest to guess the number of dimes in a jar that has a
combination of dimes and nickels. The total value in the jar is $12 and there are 15 more
nickels than dimes. How many dimes are there?
104. In your math class 70% of your grade is based on your test average and 30% on your
quiz average. Your test average is 10 points higher than your quiz average. If your average
in the 87%, what is your test average?
Homework
105. 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?
106. 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.
107. A plane flying from Newark to Los Angeles flew into a head wind, resulting in the 3000
mile trip taking 7 and a half hours. On the return trip, the plane and wind speed remained
the same, but because the plane flew with the wind the trip took only 5 hours. What was the
planes speed? (d=rt)
108. Ted is 5 years older than Cal. In three years, Cal will be 4/5 of Ted’s age. How old were
they 2 year ago?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
x=0, y=-7
x=4, y=1
x=-2, y=1
x=3, y=-1
x=9, y=-29
No solution
x=-3, y=-1
x=-3, y=1
x=1, y=3
x=-14, y=-46
x=-3, y=.5
x=-4, y=6
No solution
x=-4, y=-2
x=3, y=-1
x=2, y=-9
x=-2, y=3
x=5, y=1
x=-8, y=6
x=-1, y=4
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=8, y=0
x=7, y=10
x=-5, y=7
x=12, y=-19
Same function
Answer Key
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
x=-3, y=-9
x=19, y=-2
x=5, y=6
x=2, y=7
x=8, y=5
x=8, y=0
x=-1, y=2
x=4, y=1
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=19, y=-7
x=8, y=-5
x=-6, y=21
x=-1, y=0
x=6, y=-2
x=9, y=-4
x=8, y=-2
x=0, y=5
x=-4/3, y=15
x=3, y= -8
x=5, y=-9
x=6, y=9
x=9, y=0
65. x=5, y=-3
66. x=9, y=-5
67. x=3, y=7
68. x=23/6, y=13/2
69. x=-1, y=9
70. x=-5, y=10
71. x=8, y=3
72. No solution
73. x=-1, y=7
74. x=1, y=1
75. No solution
76. x=3, y=-3
77. x=5, y=9
78. x=8, y=7
79. x=7, y=3
80. x=2, y=3
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=7/3, y=13/3
99. x=-8, y=4
100.
x=3, y=5
101.
Adults: 620, Children: 880
102.
Plywood: $13, Box of nails: $8
103.
There are 75 dimes in the jar (90
nickels)
104.
Test average is 90% (quiz ave 80%)
105.
Pen: $0.39, Marker: $1.19
106.
Children: 607, Adults: 218
107.
Plane flew at 500mph (wind 100mph)
108.
Ted was 20 two years ago and Cal 15