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Algebra-Geometry I LINEAR SYSTEMS

SUCCESS CRITERIA:

1) Find the solution of two linear equations graphically.

2) Find the solution of two linear equations algebraically.

3) Graph two linear inequalities on the same coordinate plane.

4) Use a linear system to solve a real world problem.

INSTRUCTOR: Craig Sherman Hidden Lake High SchoolWestminster Public Schools

EMPOWER Recorded TARGET SCALE THEME

PMI-NJ Center for Teaching & Learning ~1~ NJCTL.org

MA.09.EE.04.04 Solve Systems of Equations & Inequalities

PROFICIENCY SCALE:

SCORE REQUIREMENTS

4.0 In addition to exhibiting Score 3.0 performance, in-depth inferences and applications that go BEYOND what was taught in class.

Score 4.0 does not equate to more work but rather a higher level of performance.

3.5 In addition to Score 3.0 performance, in-depth inferences and applications with partial success.o Determine the appropriate solution in a Real World example.

3.0 The learner exhibits no major errors or omissions regarding any of the information and processes (simple or complex) that were explicitly taught.

o Find the solution of two linear equations graphically, ANDo Find the solution of two linear equations algebraically , ANDo Graph two linear inequalities on the same coordinate plane, ANDo Use a linear system to solve a real world problem.

2.0 Can do one or more of the following skills / concepts: There are no major errors or omissions regarding the simpler details and processes as the

learner…o Graph two linear equations on the same coordinate plane, ORo Find the solution to a linear system by graphing, ORo Solve a linear system by using substitution, OR o Solve a linear system by using addition or subtraction, OR o Solve a linear system by using multiplication and subtraction, ORo Graph two linear inequalities on the same coordinate plane, OR o Determine the solution to a system of two linear inequalitities, OR o Use a linear system to model a real world problem, ORo Use a linear system to solve a real world problem.

1.0 Know and use the vocabulary Identify the Basic ElementsWith help, a partial understanding of some of the simpler details and process

Solve by graphing


WORD or CONCEPT DEFINITION or NOTES EXAMPLE or GRAPHIC REPRESENTATION

systems of equations

ordered pair

solution of system

point of intersection

slope

y-intercept

INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork


https://www.sophia.org/tutorials/3-1-3-2-solving-linear-systems-graphing-substituti

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/e/graphing_systems_of_equations

1. y = -x – 7

y = 43 x – 7

2. y = - 14 x + 2

y = - 12

x + 3

3. y = -3x – 5y = x + 3

4. y = -2x + 5

y = 13x – 2

5. y = -4x + 7y = -3x + 3

6. y = 34 x – 3

y = 34

x + 2

7. 3x + 2y = 2x + 2y = -2

8. x + 3y = -92x – y = -4

9. x – 2y = 2x + 4y = -8

10. 5x + y = -2x + y = 2

Homework

11. y = - 32x – 4

y = - 12 + 1

12. y = -2x – 2y = -3x – 6

13. y = x – 2y = x + 2

14. y = 34

x + 1

y = - 12

x – 4

15. y = x – 4y = -x + 2

16. x + y = 24x – y = -4

17. 4x – y = -3x + y = -2

18. x + 2y = 8x – y = 2

19. x – 3y = -32x + 3y = 12

20. 2x – 3y = 3x + 3y = -12


Solve by Substitution


substitution



https://www.sophia.org/tutorials/solving-linear-systems-by-substitution

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-linear-systems-by-substitution

Classwork

21. x = 4y – 9x = y + 3

22. 5x = -2y + 48x = -3y + 20

23. y – 4x = 28y = -2x – 2

24. y + 2x = -12y = x + 15

25. x = -2y – 72x + y = -14

26. x = 5y – 38x = -4y + 16

27. y = 2x + 34x – 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 = 0y = -3x – 18

34. x = -3y + 134x – 4y = 20

35. x = -4y + 295x + 2y = 37

36. y = -2x + 115y – 2x = 31

37. 5y – 5x = -15y = -3x + 29

38. -2x + 4y = 1x – 2y = -1

39. -6x + y = -125x + 4y = 10

40. -2x – 3y = 9-x – y = 2


Solve by Elimination (Addition & Subtraction)


elimination



https://www.sophia.org/tutorials/3-1-3-2-solving-linear-systems-graphing-substituti

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-systems-of-equations-by-elimination

Classwork

41. 3x + y = 365x + y = 56

42. x + 2y = 25x + 3y = 33

43. 3x – 5y = -52x – 5y = -34

44. 2x + 3y = 4-2x + 5y = 60

45. 2x + 2y = 25x – 2y = 40

46. -x + 2y = 14x – 2y = -11

47. 4x – y = 164x + 2y = 16

48. 2x + 5y = 5-2x + y = -23

49. 2x – 2y = -12x – 2y = -13

50. 5x + 5y = 40-5x + 3y = -40

Homework

51. 4x – y = -24x + 5y = 10

52. 2x + 4y = 10-4x + 4y = 52

53. -3x – 5y = 493x + 4y = -44

54. -4x + 3y = 395x – 3y = -45

55. -5x – 2y = -5-x – 2y = -1

56. x + 5y = -4-x + 2y = -10

57. -4x + 2y = -444x + 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)

EXAMPLE:

Classwork

61. 5x – 4y = 47-x – 16y = 125

62. 3x – 2y = 33-4x – 4y = 16

63. 2x + y = 214x + 3y = 51

64. -3x + 3y = -2712x + 5y = 108

65. 3x + 4y = 3-12x – y = -57

66. 2x + 5y = -78x + 3y = 57

67. 4x + 3y = 338x + y = 31

68. -7x – 5y = 21-10x – 8y = 24

69. 16x + 16y = -16-12x – 12y = 12

70. -6x – 10y = 2210x – 3y = -17

Homework


71. –x + y = -5-3x + 4y = -12

72. -2x – y = 2-6x + 3y = -18

73. -2x + 2y = 166x – y = -13

74. -4x – 5y = -93x + 10y = 13

75. 3x – 2y = -266x – 4y = -70

76. x + 5y = -123x + y = 6

77. x + y = 144x – 2y = 2

78. -50x + 50y = 020x – 20y = -20

79. 7x – 4y = -18-4x + 3y = 11

80. 3x + 4y = -42x – 7y = 7

Choose Your Own Strategy

NOTE: You choose which method to use (Addition, Subtraction, or Multiplication) to solve each system.

Classwork

81. –x + 4y = 5x + 4y = 11

82. 3x – y = 74x – 2y = 8

83. 2y + 5x = 35y = 4x – 28

84. 5x – 4y = -39-3x – 4y = -15

85. y = -5x + 594x + y = 49

86. y = x + 6

y = 45 x + 6

87. -2x + 4y = 28

2x – 3y = -18

88. y = -x + 123y + 3x = 36

89. 2x + 4y = -10-4x – 12y = 36

90. –x – 5y = -3-2x + 5y = 9

Homework

91. -3x + 5y = -3912x – 4y = 60

92. y = 3x – 18y – 3x = -24

93. x + 3y = 16-x + 4y = 5

94. x = -3y – 19x + 5y = -22

95. 3x – 3y = 129x + 2y = 102

96. y = - 43 x + 4


y = 23

x + 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?


https://www.sophia.org/tutorials/using-systems-of-equations-to-make-decisions

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-linear-functions-modeling/v/exploring-linear-relationships

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


inequality

solution of system



https://www.sophia.org/tutorials/solving-linear-inequalities-by-graphing--5

https://www.khanacademy.org/math/algebra-basics/core-algebra-graphing-lines-slope/core-algebra-graphing-linear-inequalities/v/graphing-inequalities

Classwork

105. y ≤ 52

x – 2

y ≥ 12

x + 2

106. y ≤ 14

x – 1

y ¿ 5x – 5

107. y ¿ - 13

x – 3

y ≤ 53

x + 3

108. y > 2x – 5 3x + 4y < 12

109. x + y ≥ - 3 5x – y ≤ -3

Homework

110. y ¿ 12

x + 2

y > 3x – 3

111. y ≥ -x + 5y ≤ 3x – 4

112. y < 14

x

y ≤ -x + 4

113. y > 2x +42x – y ≤ 4

114. 3x – y ≥ - 1x + y ≤ -3

Solving Systems of Linear Equations & Inequalities 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 toa. 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 = 7x - 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 gi r 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 play as a fundraiser. The student t ickets cost $2.00 each and the adul t t ickets cost $4 each. They sold 5 t imes as many student t ickets as adul t t ickets. They made $140. How many student 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.


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