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Math Help - Systems of equations help

  1. #1
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    Systems of equations help

    This seems like it requires a lot of intuition because I'm always having trouble figuring the right answers and get different answers...

    Like here:

    3x-5y+5z = 1
    -5x-2y+3z = 0
    7x-y+3z = 0


    My work:

    -5x-2y+3z = 0
    -7x+y-3z = 0

    -12x-y = 0
    7x +y+3z = 0
    <br />
-5x+3z = 0
    5x+2y-3z=0
    2y = 0

    Inconsistent. And this isn't how you do it and I don't know why what I'm doing is wrong.
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  2. #2
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    if i understand you correctly

    Quote Originally Posted by A Beautiful Mind View Post
    This seems like it requires a lot of intuition because I'm always having trouble figuring the right answers and get different answers...

    Like here:

    3x-5y+5z = 1
    -5x-2y+3z = 0
    7x-y+3z = 0


    My work:

    -5x-2y+3z = 0
    -7x+y-3z = 0

    -12x-y = 0
    7x +y+3z = 0
    <br />
-5x+3z = 0
    5x+2y-3z=0
    2y = 0

    Inconsistent. And this isn't how you do it and I don't know why what I'm doing is wrong.
    if i understand you correctly you are eventually trying to find what each variable equals and the way to do that with a system of equations is to find what each variable equals all with one variable in it such as finding what y equals in terms of x and what z equals in terms of x.

    Then insert those equalities into one of the original questions and find what x truly equals.

    then plug this number into your equalities for y and z and there you have it.

    I hope this answers your question and truly helps
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  3. #3
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    Quote Originally Posted by A Beautiful Mind View Post
    This seems like it requires a lot of intuition because I'm always having trouble figuring the right answers and get different answers...
    Like here:
    3x-5y+5z = 1
    -5x-2y+3z = 0
    7x-y+3z = 0


    My work:

    -5x-2y+3z = 0
    -7x+y-3z = 0 <-- OK
    -12x-y = 0

    7x +y+3z = 0 <-- not consistent

    -5x+3z = 0
    5x+2y-3z=0
    2y = 0

    Inconsistent. And this isn't how you do it and I don't know why what I'm doing is wrong.

    In your "work" you correctly handled the sign for the variables on the Left Hand Side the FIRST TIME.

    However, I don't understand why you changed the sign of the y variable and did not change ALL of the Left Hand Side the second time.

    It looks as if you understand what you are supposed to do.
    Just "watch those signs"
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  4. #4
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    Quote Originally Posted by A Beautiful Mind View Post
    This seems like it requires a lot of intuition <<<< definitely no
    because I'm always having trouble figuring the right answers and get different answers...

    Like here:

    3x-5y+5z = 1
    -5x-2y+3z = 0
    7x-y+3z = 0

    ...
    1. Choose the variable which you want to eliminate in all (3) equations. You started with z. You used the equations #2 and #3. Now do the same with #1 and #2. Multiply the equ.#1 by the leading factor of z of the equ.#2 and multiply the equ.#2 by the leading factor of z of equ.#1:
    \left|\begin{array}{rcl}3x-5y+5z&=&1 / \cdot (3) \\ -5x-2y+3z&=& 0 / \cdot (5)\end{array}\right. \implies \left|\begin{array}{rcl}9x-15y+15z&=&3  \\ -25x-10y+15z&=& 0  \end{array}\right.
    Now subtract columnwise:
    34x-5y=3

    2. You now have a system of 2 equations in (x,y):

    \left|\begin{array}{rcl}-12x-y &=& 0 \\ 34x-5y&=&3 \end{array}\right.

    Choose the variable you want to eliminate. I guessed that you have chosen y.
    Multiply the equ.#1 by the leading factor of y of the equ.#2 and multiply the equ.#2 by the leading factor of y of equ.#1:

    \left|\begin{array}{rcl}-12x-y &=& 0 / \cdot (-5) \\ 34x-5y&=&3 / \cdot (-1) \end{array}\right. \implies \left|\begin{array}{rcl}60x+5y &=& 0  \\ -34x+5y&=&-3 \end{array}\right.
    Subtract columnwise:
    94x = 3

    3. Solve for x: 94x = 3~\implies~x=\frac3{94}

    4. Plug in this value into one of the equations at 2. to calculate y. Afterwards plug in the values for x and y into one of the equations at 1. to calculate z.

    5. Done!
    Last edited by earboth; November 29th 2009 at 01:20 AM. Reason: typo
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