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Math Help - system of linear equations question

  1. #1
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    system of linear equations question

    Hello, I have the following set of three linear equations. I am trying to solve for x,y,z using substitution.

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

    My first step is to isolate 'y=z-x'
    I then substitute y into the next two equations resulting in:

    -3x + 2z = 0
    -3x + z = 3

    Now when I subtract these I get z = -3, however the answer should be z = 3.
    What am I doing wrong here ?

    Thanks kindly for any help.
    Last edited by fran1942; April 18th 2011 at 09:00 PM.
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  2. #2
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    Surely when you subtract the two final equations (which by the way is NOT the substitution method), the x terms are eliminated leaving z = -3...
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  3. #3
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    sorry, my typo. I was meaning z = -3.
    The actual answer should be z = 3.

    Can you please tell me where I am going wrong. How am I getting z = -3, instead of z = 3 ?

    Thanks kindly.
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  4. #4
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    -2x + 4y = 0 is equivalent to x - 2y = 0, i.e. x = 2y. Since x - y - z = 0, substitute x = 2y and we get 2y - y - z = y - z = 0, i.e. y = z. Since 3y - 2z = 3, substitute y = z and we get 3z - 2z = z = 3.
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