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3.5 – Solving Systems of Equations in Three Variables

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

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3.5 – Solving Systems of Equations in Three Variables

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  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)

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