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Oct. 21 - Substitution & Graphing

algebra 1<br>middle and high school math<br>system of equations

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Oct. 21 - Substitution & Graphing

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  1. national color day! 10.21.22 Take out your spiral for a warm-up. Agenda: • Warm-up • Solving Word Problems • Beat the Bolts If animals could talk, which one would be the rudest? Calculator, Pencil, Spiral

  2. Warm-up: Solve each system using substitution. 1. -6x - y = 12 y = 4x + 18 2. 5x - 12y = 14 x = 12y - 42

  3. Warm-up: Solve each system using substitution. 1. -6x - y = 12 y = 4x + 18 2. 5x - 12y = 14 x = 12y - 42

  4. Warm-up: Solve each system using substitution. 1. -6x - y = 12 y = 4x + 18 2. 5x - 12y = 14 x = 12y - 42

  5. Linear Systems

  6. Write a system of equations for the problem situation. Solve the system using substitution method. #1 You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same?

  7. You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? Is this a slope-intercept or standard form scenario?

  8. You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? Slope-intercept: There is a rate of change described in each job scenario.

  9. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Define the variables.

  10. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Define the variables.

  11. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Define the variables.

  12. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Write the equations.

  13. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Write the equations.

  14. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Write the equations.

  15. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Since they both equal y, they equal each other.

  16. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Solve the equation.

  17. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Solve the equation.

  18. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Solve the equation.

  19. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Solve the equation.

  20. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Solve the equation.

  21. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Plug back into one of the equations.

  22. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Plug back into one of the equations.

  23. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Plug back into one of the equations.

  24. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Plug back into one of the equations.

  25. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Write a sentence to explain what the solution means.

  26. Let x = number of hours worked y = total earnings You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Write a sentence to explain what the solution means.

  27. ANSWER #1 You are looking for an after school job. One job pays $9 per hour. Another job pays $12 per hour, but you must purchase a uniform that costs $39. After how many hours would your net earnings from either job be the same?

  28. Write a system of equations for the problem situation. Solve the system using substitution method. A cell phone provider offers two different monthly services. Plan A costs $40 per month plus $0.20 per text message sent or received. Plan B costs $60 per month but has unlimited text messaging. How many texts must be sent for the plans to cost the same? What will be the cost? #2

  29. #2 ANSWER A cell phone provider offers two different monthly services. Plan A costs $40 per month plus $0.20 per text message sent or received. Plan B costs $60 per month but has unlimited text messaging. How many texts must be sent for the plans to cost the same? What will be the cost?

  30. Write a system of equations for the problem situation. Solve the system using substitution method. You might need to re-write one of your equations. A snack bar sells two sizes of snack packs. A large snack pack is $5, and a small snack pack is $3. In one day, the snack bar sold 60 snack packs for a total of $220. How many of each size snack pack did the snack bar sell? #3

  31. #3 ANSWER A snack bar sells two sizes of snack packs. A large snack pack is $5, and a small snack pack is $3. In one day, the snack bar sold 60 snack packs for a total of $220. How many of each size snack pack did the snack bar sell?

  32. Write a system of equations for the problem situation. Solve the system using substitution method. You might need to re-write one of your equations. #4 Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. How many adults and how many children were in the group?

  33. #4 ANSWER Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. How many adults and how many children were in the group?

  34. Write a system of equations for the problem situation. Solve the system using substitution method. You might need to re-write one of your equations. A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? #5

  35. A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? Is this a slope-intercept or standard form scenario?

  36. A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? Standard Form: There are two unknowns with no rate of change described.

  37. Let b = number of hours worked v = total earnings A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Define the variables.

  38. Let b = number of buses needed v = total earnings A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Define the variables.

  39. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? y = 9x y = 12x - 39 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Define the variables.

  40. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 Working for 13 hours will result in the same earnings of $117. Write the equations.

  41. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 Working for 13 hours will result in the same earnings of $117. Write the equations.

  42. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 Working for 13 hours will result in the same earnings of $117. Write the equations.

  43. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 Working for 13 hours will result in the same earnings of $117. Isolate a variable so that substitution can be used.

  44. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 b + v = 6 Working for 13 hours will result in the same earnings of $117. Isolate a variable so that substitution can be used.

  45. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 b + v = 6 -b -b Working for 13 hours will result in the same earnings of $117. Isolate a variable so that substitution can be used.

  46. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 b + v = 6 -b -b v = 6 - b Working for 13 hours will result in the same earnings of $117. Isolate a variable so that substitution can be used.

  47. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 b + v = 6 -b -b v = 6 - b Working for 13 hours will result in the same earnings of $117. Use substitution to solve for the variables.

  48. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 51b + 10(6 - b) = 142 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 b + v = 6 -b -b v = 6 - b Working for 13 hours will result in the same earnings of $117. Use substitution to solve for the variables.

  49. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 51b + 10(6 - b) = 142 51b + 60 - 10b = 142 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 b + v = 6 -b -b v = 6 - b Working for 13 hours will result in the same earnings of $117. Use substitution to solve for the variables.

  50. Let b = number of buses needed v = number of vans needed A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. How many buses and vans will be needed? 51b + 10(6 - b) = 142 51b + 60 - 10b = 142 41b + 60 = 142 9x = 12x - 39 -12x -12x -3x = -39 -3 -3 x = 13 y = 9x y = 9(13) y = 117 b + v = 6 51b + 10v = 142 b + v = 6 -b -b v = 6 - b Working for 13 hours will result in the same earnings of $117. Use substitution to solve for the variables.

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