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Oct. 26 - Best Method & Multiple Method

algebra 1<br>middle and high school math<br>system of equations choosing the best method

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Oct. 26 - Best Method & Multiple Method

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  1. black cat day! 10.26.22 Let’s do our drawing from yesterday! Take out your spiral. Would you rather have no more homework or no more tests? Agenda: • Envelope Drawing • Notes: Best Method/Multiple Method • Practice Calculator, Pencil, Spiral

  2. Envelope Challenge

  3. Work in groups of one, two, or three people. Write your name(s) on one side of your ticket. Show your work on the ticket. Circle the final answer. Fold your ticket in half and place in envelope. If you need the ticket back, ask the teacher. Tickets will be pulled at random. First correct answer with work wins. You can win more than once. Let’s find our winning teams!!! Envelope Challenge Rules

  4. Skittles and Starbursts #1 Micha and Danielle are at the candy store and decide to buy Skittles and Starbursts. Micha spends $4.65 to purchase three bags of Skittles and 4 packages of Starbursts. Danielle spends $6.15 to purchase 5 bags of Skittles and 4 packages of Starbursts. Write and solve a system of equations to determine the cost of 1 bag of Skittles and 1 bag of Starbursts.

  5. Skittles and Starbursts #1 Micha and Danielle are at the candy store and decide to buy Skittles and Starbursts. Micha spends $4.65 to purchase three bags of Skittles and 4 packages of Starbursts. Danielle spends $6.15 to purchase 5 bags of Skittles and 4 packages of Starbursts. Write and solve a system of equations to determine the cost of 1 bag of Skittles and 1 bag of Starbursts.

  6. Get a Job! #2 You are looking for a carpentry apprentice. One job pays $16 per hour. Another job pays $20 per hour, but you must purchase tools that costs $600. After how many hours would your earnings from either job be the same? What is the amount when they are the same?

  7. Get a Job! #2 You are looking for a carpentry apprentice. One job pays $16 per hour. Another job pays $20 per hour, but you must purchase tools that costs $600. After how many hours would your earnings from either job be the same? What is the amount when they are the same?

  8. #3 Pencils and Pens Miss Farnsworth has noticed that several of her students have been coming to class without pens or pencils. She has decided to start selling them in class. Terence decided to buy 2 pencils and 3 pens of a total of $1.55. Erica purchased 3 pencils and 4 pens for the price of $2.15. Write a system of equations to model Terrence's and Erica's purchases and then determine the cost of a pencil and the cost of a pen.

  9. #3 Pencils and Pens Miss Farnsworth has noticed that several of her students have been coming to class without pens or pencils. She has decided to start selling them in class. Terence decided to buy 2 pencils and 3 pens of a total of $1.55. Erica purchased 3 pencils and 4 pens for the price of $2.15. Write a system of equations to model Terrence's and Erica's purchases and then determine the cost of a pencil and the cost of a pen.

  10. What's Your Age? #4 Rema is older than Ken. The difference of their ages is 12 and the sum of their ages is 50. How old is each person?

  11. What's Your Age? #4 Rema is older than Ken. The difference of their ages is 12 and the sum of their ages is 50. How old is each person?

  12. #5 Boots and Heels Mrs. Henry is taking advantage of the holiday sales at a local shoe store. On Thursday, she purchase 2 pairs of boots and 3 pairs of high heels and spends $215.97. On Friday, she decides to go back and buy another pair of boots and another pair of high heels and spends $88.49. Write a system of equations to model Mrs. Henry's purchases and then determine the cost of a pair of boots and the cost of a pair of high heels.

  13. #5 Boots and Heels Mrs. Henry is taking advantage of the holiday sales at a local shoe store. On Thursday, she purchase 2 pairs of boots and 3 pairs of high heels and spends $215.97. On Friday, she decides to go back and buy another pair of boots and another pair of high heels and spends $88.49. Write a system of equations to model Mrs. Henry's purchases and then determine the cost of a pair of boots and the cost of a pair of high heels.

  14. Numbers Please! #6 The sum of two numbers is 70. One number is ten more than twice the other number. What are the two numbers?

  15. Numbers Please! #6 The sum of two numbers is 70. One number is ten more than twice the other number. What are the two numbers?

  16. #7 Auto Parts Alejandro is a forklift operator in an auto parts warehouse. He recently loaded a truck with 5 cartons of tires and 3 cartons of cylinders for a total weight of 525 pounds. He loaded another truck with 3 cartons of tires and 3 cartons of cylinders for a total weight of 375 pounds. Write a system of equations to model the contents of each of the trucks and then determine the weight of a carton of tires and the weight of a carton of cylinders.

  17. #7 Auto Parts Alejandro is a forklift operator in an auto parts warehouse. He recently loaded a truck with 5 cartons of tires and 3 cartons of cylinders for a total weight of 525 pounds. He loaded another truck with 3 cartons of tires and 3 cartons of cylinders for a total weight of 375 pounds. Write a system of equations to model the contents of each of the trucks and then determine the weight of a carton of tires and the weight of a carton of cylinders.

  18. Garden Dimensions #8 The length of Sally's garden is 4 meters greater than 3 times the width. The perimeter of the garden is 72 meters. What are the length and width of the garden?

  19. Garden Dimensions #8 The length of Sally's garden is 4 meters greater than 3 times the width. The perimeter of the garden is 72 meters. What are the length and width of the garden?

  20. Taxi Rides #9 Turbo Taxi Company charges $5 for a pickup and $0.75 per mile. Cool Cab Company charges $4.00 for a pickup and $0.95 per mile. For what number of miles is the cost the same, and what is that cost?

  21. Taxi Rides #9 Turbo Taxi Company charges $5 for a pickup and $0.75 per mile. Cool Cab Company charges $4.00 for a pickup and $0.95 per mile. For what number of miles is the cost the same, and what is that cost?

  22. Cable TV #10 A cable TV company offers two different pricing plans. Plan A charges $11.25 per month plus a one-time installation fee of $120. Plan B charges $18.75 per month plus a one-time installation fee of $60. For how many months is the price the same for both plans, and what is that price?

  23. Cable TV #10 A cable TV company offers two different pricing plans. Plan A charges $11.25 per month plus a one-time installation fee of $120. Plan B charges $18.75 per month plus a one-time installation fee of $60. For how many months is the price the same for both plans, and what is that price?

  24. Systems of Equations - Choose the Best Method

  25. Identify the Best Method Graphing, Substitution, or Elimination #1 -3x - 3y = 3 y = -5x - 17

  26. Identify the Best Method Graphing, Substitution, or Elimination #1 -3x - 3y = 3 y = -5x - 17 Substitution because in the second equation, the y-variable is already isolated.

  27. Identify the Best Method Graphing, Substitution, or Elimination #2 y = 4x + 3 y = -x - 2

  28. Identify the Best Method Graphing, Substitution, or Elimination #2 y = 4x + 3 y = -x - 2 Graphing because both equations are solved for y and the numbers will easily fit on a graph.

  29. Identify the Best Method Graphing, Substitution, or Elimination #3 x = 7 y = -x +9

  30. Identify the Best Method Graphing, Substitution, or Elimination #3 x = 7 y = -x +9 Substitution because in the first equation, the x-variable is already isolated (and solved).

  31. Identify the Best Method Graphing, Substitution, or Elimination #4 4x - 2y = 8 y = -2

  32. Identify the Best Method Graphing, Substitution, or Elimination #4 4x - 2y = 8 y = -2 Substitution because in the second equation, the y-variable is already isolated (and solved).

  33. Identify the Best Method Graphing, Substitution, or Elimination #5 y = -2x +2 y = -2x - 2

  34. Identify the Best Method Graphing, Substitution, or Elimination #5 y = -2x +2 y = -2x - 2 Graphing because both equations are solved for y and the numbers will fit nicely on a graph. Notice, we can quickly solve without graphing since the slopes are equal but the y-intercepts are different: no solution.

  35. Identify the Best Method Graphing, Substitution, or Elimination #6 y = 6x -11 -2x - 3y = -7

  36. Identify the Best Method Graphing, Substitution, or Elimination #6 y = 6x -11 -2x - 3y = -7 Substitution because in the first equation, the y-variable is already isolated.

  37. Identify the Best Method Graphing, Substitution, or Elimination #7 y = -2 4x - 3y = 18

  38. Identify the Best Method Graphing, Substitution, or Elimination #7 y = -2 4x - 3y = 18 Substitution because in the first equation, the y-variable is already isolated (and solved).

  39. Identify the Best Method Graphing, Substitution, or Elimination #8 y = 2x - 3 y = -3x + 2

  40. Identify the Best Method Graphing, Substitution, or Elimination #8 y = 2x - 3 y = -3x + 2 Graphing because both equations are solved for y and the numbers will easily fit on a graph.

  41. Identify the Best Method Graphing, Substitution, or Elimination #9 -5x + y = - 3 3x -8y = 24

  42. Identify the Best Method Graphing, Substitution, or Elimination #9 -5x + y = - 3 3x -8y = 24 Elimination because both equations are in standard form. We could multiply the top equation by 8 to start the solve.

  43. Identify the Best Method Graphing, Substitution, or Elimination #10 -4x + y = -6 -5x -y = 21

  44. Identify the Best Method Graphing, Substitution, or Elimination #10 -4x + y = -6 -5x -y = 21 Elimination because both equations are in standard form. The coefficients of y are already opposites, so we can add as our first step.

  45. Solving Using Multiple Methods y = 3x + 10 5x + 5y = -30 Substitution Elimination Graphing The best method for this problem is because:

  46. Solving Using Multiple Methods y = 3x + 10 5x + 5y = -30 Substitution Elimination Graphing The best method for this problem is because:

  47. Solving Using Multiple Methods -2x + 6y = -12 y = -2x + 5 Substitution Elimination Graphing The best method for this problem is because:

  48. Solving Using Multiple Methods -2x + 6y = -12 y = -2x + 5 Substitution Elimination Graphing The best method for this problem is because:

  49. Solving Using Multiple Methods 9y = -2x + 12 y = -2/9x + 3 Substitution Elimination Graphing The best method for this problem is because:

  50. Solving Using Multiple Methods 9y = -2x + 12 y = -2/9x + 3 Substitution Elimination Graphing The best method for this problem is because:

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