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help with solving the system of equations

3x+4y+z=7
2y+z=3
-5x+3y+8z=-31

  • math -

    the middle equation is nice and gives us
    z = 3-2y
    sub that into the first and third

    1) 3x + 4y + 3 - 2y = 7
    3x + 2y = 4 (#1)

    3) -5x + 3y + 8(3-2y) = -31
    -5x + 3y + 24 - 16y = -31
    -5x - 13y = -55
    5x + 13y = 55 (#3)

    #1 by 5: 15x + 10y = 20
    #3 by 3: 15x + 39y = 165

    subtract them ...
    29y = 145
    y = 5

    back in #1
    3x + 2y = 4
    3x + 10 = 4
    x = -2

    back into the middle
    2y + z = 3
    10 + z = 3
    z = -7

    x = -2, y = 5, z = -7

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