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Methods for Solving Systems of Linear Equations: Graphing, Substitution, and Elimination Strategies

This educational resource explores various methods for solving systems of linear equations, including graphing, substitution, and elimination techniques. We delve into the conditions for solutions such as parallel lines (no solutions), coinciding lines (infinitely many solutions), and intersecting lines (one solution). The guide provides examples, definitions, and problem-solving strategies to help students understand these foundational concepts in algebra. Perfect for learners seeking clarity on these essential techniques.

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Methods for Solving Systems of Linear Equations: Graphing, Substitution, and Elimination Strategies

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Presentation Transcript

  1. With Mr. Tyler

  2. Describe the Line.

  3. Graphing

  4. Elimination (add/subtract)

  5. Substitution

  6. Elimination (multiply)

  7. Best Method

  8. Describe the Line Elimination (add/subtract) Elimination (multiply) Best Method Graphing Substitution $100 $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 $500

  9. 1-100 1 - 100 These lines do not intersect. $100

  10. 1-100A 1 - 100 What is "parallel"? $100

  11. 1-200 These lines overlap completely. $200

  12. 1-200A 1 - 100 What is "coinciding"? $200

  13. 1-300 These lines produce no solution. $300

  14. 1-300A 1 - 100 What is "parallel"? $300

  15. 1-400 These lines produce 1 solution. $400

  16. 1-400A 1 - 100 What is "intersecting"? $400

  17. 1-500 These lines produce infinitely many solutions. $500

  18. 1-500A 1 - 100 What is "coinciding Or overlapping each other"? $500

  19. 2-100 1 - 100 Find the solution. $100

  20. 2-100A 1 - 100 What is "(0, -1)"? $100

  21. 2-200 Find the solution. $200

  22. 2-200A 1 - 100 What is "(1, 2)"? $200

  23. 2-300 Find the solution. $300

  24. 2-300A 1 - 100 What is "(-1, 3)"? $300

  25. 2-400 Find the solution. $400

  26. 2-400A 1 - 100 What is "no solution"? $400

  27. 2-500 Find the solution. $500

  28. 2-500A 1 - 100 What is "infinite solutions"? $500

  29. 3-100 1 - 100 Find x. x + y = 8 x - y = 4 $100

  30. 3-100A 1 - 100 What is "x = 6"? $100

  31. 3-200 Find r. 2r + s = 5 r - s = 1 $200

  32. 3-200A 1 - 100 What is "r = 2"? $200

  33. 3-300 Find y. x - 3y = 7 x + 2y = 2 $300

  34. 3-300A 1 - 100 What is "y = -1"? $300

  35. 3-400 Find x. 3x + y = 1 x - y = 3 $400

  36. 3-400A 1 - 100 What is "x = 1"? $400

  37. 3-500 Find x. 5x + 4y = 12 3x + 4y = 4 $500

  38. 3-500A 1 - 100 What is "x = 4"? $500

  39. 4-100 1 - 100 Find x. y = 3 x + y = 7 $100

  40. 4-100A 1 - 100 What is "x = 4"? $100

  41. 4-200 Find y. y = 5x x + 2y = 22 $200

  42. 4-200A 1 - 100 What is "y = 10"? $200

  43. 4-300 Find y. x = -2 x - 2y = 6 $300

  44. 4-300A 1 - 100 What is "y = -4"? $300

  45. 4-400 Find x. x + y = 4 y = 3x $400

  46. 4-400A 1 - 100 What is "x = 1"? $400

  47. 4-500 Find x. -3x + y = - 8 y = 4 - x $500

  48. 4-500A 1 - 100 What is "x = 3"? $500

  49. 5-100 1 - 100 What would you multiply the 1st equation by to eliminate y? 2x + y = 5 3x - 2y = 4 $100

  50. 5-100A 1 - 100 What is "2"? $100

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