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6.1 – Graphing Systems of Equations

6.1 – Graphing Systems of Equations. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.

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6.1 – Graphing Systems of Equations

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  1. 6.1 – Graphing Systems of Equations

  2. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.

  3. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

  4. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

  5. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

  6. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

  7. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

  8. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

  9. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. y = -x + 1 y = x – 3 y = -x – 2

  10. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

  11. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

  12. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

  13. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 2 2 2 y = -x + 1 y = x – 3 y = -x – 2

  14. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  15. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  16. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  17. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. y = -x + 1 y = x – 3 y = -x – 2

  18. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  19. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  20. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 2 2 2 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  21. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  22. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  23. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  24. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

  25. Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x – 2 Infinite Sol. y = -x + 1 y = x – 3 y = -x – 2

  26. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 y = -2x – 1

  27. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2 y = -2x – 1

  28. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

  29. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

  30. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

  31. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

  32. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

  33. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

  34. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2

  35. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

  36. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

  37. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

  38. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

  39. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

  40. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

  41. Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1 One sol. @ (0,-1)

  42. b. 2x + 3y = 6 -4x – 6y = -12

  43. b. 2x + 3y = 6 3y = -2x + 6 -4x – 6y = -12

  44. b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 -4x – 6y = -12

  45. b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 3 -4x – 6y = -12

  46. b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

  47. b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

  48. b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

  49. b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

  50. b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

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