algebra

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systems of linear equations in 3 variables

1/3x-2/3y+z=0
1/2x-3/4y+z=1/4
-2x-y+z=1

  • algebra -

    Mult 1st eq by 3; x-2y+3z = 0
    Mult 2nd eq by 4: 2x - 3y + 4z = 1
    Add 2nd and 3rd: -4y+5z = 2
    Mut 1st by 2: 2x-4y + 6z = 0
    Add that answer and 3rd eq: -5y + 7z = 1
    5(-4y + 5z = 2) + -4(-5y + 7z = 1)
    -20y + 25z = 10 + 20y - 28z = -4
    -3z =6
    z = -2
    Sub into the 1st eq: x - 2y -6 =0
    Sub into the 3rd eq: -2x-y-2 = 1
    2(x-2y = 6) + (-2x-y=3)
    2x - 4y = 12 + -2x -y = 3
    -5y =15
    y = -3
    sub into the 3rd eq
    -2x -(-3) +(-2) = 1
    -2x +1 = 1
    x = 0
    (0,-3,-2)

  • algebra -

    It might be easier if you
    a) multiplied the first equation by 3
    b) the second equation by 4

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