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15 February, 04:31

Solve the system of equations. 4x+2y+5z=8 5x+3y+4z=9 6x+3y+3z=3

A) (x=-3, y=6, z=1)

B) (x=-5, y=8, z=3)

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Answers (1)
  1. 15 February, 07:33
    0
    x = - 4, y = 7, z = 2.

    Step-by-step explanation:

    4x + 2y + 5z = 8 ... (1)

    5x + 3y + 4z = 9 ... (2)

    6x + 3y + 3z = 3 ... (3)

    Subtract: equation (2) - equation (3):

    -x + z = 6 ... (4)

    Multiply (1) by 3 and (2) by 2:

    12x + 6y + 15z = 24 ... (5)

    10x + 6y + 8z = 18 ... (6)

    Subtract: (5) - (6):

    2x + 7z = 6 ... (7)

    Multiply equation (4) by 2:

    - 2x + 2z = 12 ... (8)

    Add (7) + (8):

    9z = 18, so z = 2.

    Substitute for z in equation (4)

    -x + 2 = 6

    -x = 4 so x = - 4.

    Now find y by substituting in equation (1):

    4 (-4) + 2y + 5 (2) = 8

    2y = 8 + 16 - 10 = 14

    y = 7.
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