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Example:Solve the following system:

8x + 10z = 7y + 15
2x + 3y + 8z = 7
5y + 9 = 4x + 2z
  1. Rearrange the system:
    8x - 7y + 10z = 15
    2x + 3y + 8z = 7
    -4x + 5y - 2z = - 9
  2. Create the matrices:

    D =    


    Dx =    

    Dy =    

    Dz =    

  3. Find the determinants:

    detD = (- 48 + 224 + 100) - (- 120 + 320 + 28) = 276 - 228 = 48
    detDx = (- 90 + 504 + 350) - (- 270 + 600 + 98) = 764 - 428 = 336
    detDy = (- 112 - 480 - 180) - (- 280 - 576 - 60) = - 772 - (- 916) = 144
    detDz = (- 216 + 196 + 150) - (- 180 + 280 + 126) = 130 - 226 = - 96

  4. x = = 7. y = = 3. z = = - 2.
Thus, (x, y, z) = (7, 3, - 2).

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