1 / 37

Efficient Methods for Solving Systems of Equations in Three Variables

Explore step-by-step techniques and strategies to solve complex systems of equations in three variables effortlessly. Master the process with practical examples and clear explanations.

kaseem-rios
Télécharger la présentation

Efficient Methods for Solving Systems of Equations in Three Variables

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3.5 – Solving Systems of Equations in Three Variables

  2. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

  3. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

  4. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2x – y + 3z = - 5

  5. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5]

  6. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x + 2y + z = 10 4x – 2y + 6z = -10

  7. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x+ 2y + z = 10 4x– 2y + 6z = -10 5x + 7z = 0

  8. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x+ 2y + z = 10 4x– 2y + 6z = -10 5x + 7z = 0

  9. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

  10. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2x – y + 3z = - 5 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

  11. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2x – y + 3z = - 5 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x+ 2y + z = 10 4x– 2y + 6z = -10 5x + 7z = 0

  12. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

  13. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -10 2x – 3y – 5z = 27 5x + 7z = 0

  14. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x+ 3y – 9z = 15 4x – 2y + 6z = -102x– 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

  15. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x+ 3y – 9z = 15 4x – 2y + 6z = -102x– 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

  16. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -102x – 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

  17. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -102x – 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

  18. 5x + 7z = 0 -4x – 14z = 42 5x + 7z = 0 -4x – 14z = 42

  19. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42

  20. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x+ 14z = 0 -4x– 14z = 42 6x = 42

  21. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x+ 14z = 0 -4x– 14z = 42 6x = 42

  22. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7

  23. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0

  24. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0

  25. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0

  26. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0 - 7z = -35

  27. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0 7z = -35 z = -5

  28. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0 7z = -35 z = -5

  29. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

  30. 3.5 – Solving Systems of Equations in Three Variables Ex.x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

  31. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 35 + 7z = 0 7z = -35 z = -5

  32. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5= 10 35 + 7z = 0 7z = -35 z = -5

  33. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5= 10 35 + 7z = 0 2y + 2 = 10 7z = -35 z = -5

  34. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5= 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5

  35. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5= 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5y = 4

  36. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5= 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5y = 4

  37. 5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5= 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5y = 4 (7,4,-5)

More Related