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6.5 – Applying Systems of Linear Equations

6.5 – Applying Systems of Linear Equations. Ex. 1 3 x + 4 y = -25 2 x – 3 y = 6. Ex. 1 3 x + 4 y = -25 2 x – 3 y = 6 Eliminate “ x ” OR Eliminate “ y ”. Ex. 1 3 x + 4 y = -25 2 x – 3 y = 6 Eliminate “ x ”. Ex. 1 3 x + 4 y = -25

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6.5 – Applying Systems of Linear Equations

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  1. 6.5 – Applying Systems of Linear Equations

  2. Ex. 1 3x + 4y = -25 2x – 3y = 6

  3. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x”OR Eliminate “y”

  4. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x”

  5. Ex. 13x + 4y = -25 2x – 3y = 6 Eliminate “x”

  6. Ex. 12[3x + 4y = -25] -3[2x – 3y = 6] Eliminate “x”

  7. Ex. 12[3x + 4y = -25] -3[2x – 3y = 6] Eliminate “x” 6x + 8y = -50 -6x +9y = -18

  8. Ex. 1 2[3x + 4y = -25] -3[2x – 3y = 6] Eliminate “x” 6x + 8y = -50 -6x +9y = -18

  9. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = -18 17y = -68

  10. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = -1817y = -68 17 17

  11. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = -1817y = -68 17 17 y = -4

  12. Ex. 13x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  13. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x”OR Eliminate “y” 6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  14. Ex. 1 3x+ 4y = -25 2x– 3y = 6 Eliminate “x”OR Eliminate “y” 6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  15. Ex. 13[3x + 4y = -25] 4[2x – 3y = 6] Eliminate “x”OR Eliminate “y” 6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  16. Ex. 13[3x + 4y = -25] 4[2x – 3y = 6] Eliminate “x”OR Eliminate “y” 6x + 8y = -50 9x + 12y = -75 -6x +9y = -188x – 12y = 24 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  17. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x”OR Eliminate “y” 6x + 8y = -50 9x + 12y = -75 -6x +9y = -188x – 12y = 24 17y = -68 17x = -51 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  18. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x”OR Eliminate “y” 6x + 8y = -50 9x + 12y = -75 -6x +9y = -188x – 12y = 24 17y = -6817x = -51 17 17 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  19. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x”OR Eliminate “y” 6x + 8y = -50 9x + 12y = -75 -6x +9y = -188x – 12y = 24 17y = -6817x = -51 17 17 17 17 y = -4 x = -3 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 +16 +16 3x= -9 3 3 x = -3 (-3, -4)

  20. Ex. 1 3x + 4y = -25 2x – 3y = 6 Eliminate “x”OR Eliminate “y” 6x + 8y = -50 9x + 12y = -75 -6x +9y = -188x – 12y = 24 17y = -6817x = -51 17 17 17 17 y = -4 x = -3 3x + 4y = -25 3x + 4y = -25 3x + 4(-4) = -25 3(-3) + 4y = -25 3x – 16 = -25 -9 + 4y = -25 +16 +16+9 +9 3x= -94y = -16 3 3 4 4 x = -3 y = -4 (-3, -4)

  21. Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12 x + 2y = 14

  22. Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12 -4[x + 2y = 14]

  23. Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12 -4[x + 2y = 14] 4x – 3y = 12

  24. Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12 -4[x + 2y = 14] 4x – 3y = 12 -4x – 8y = -56

  25. Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12 -4[x + 2y = 14] 4x – 3y = 12 4x – 3(4) = 12 -4x – 8y = -56 4x – 12 = 12 -11y = -44 4x = 24 y = 4x = 6 (6,4)

  26. Ex.3 3x – 7y = -14 5x + 2y = 45

  27. Ex.3 3x – 7y = -14 5x + 2y = 45 2[3x – 7y = -14]5[3x – 7y = -14] 7[5x + 2y = 45]-3[5x + 2y = 45] 6x– 14y = -28 15x– 35y = -70 35x+ 14y = 315-15x– 6y = -135 41x = 287 -41y = -205 x = 7 y = 5 3x – 7y = -14 3x – 7y = -14 3(7) – 7y = -14 3x – 7(5) = -14 21 – 7y = -14 3x – 35 = -14 -7y = -35 3x = 21 y = 5 (7,5) x = 7

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