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Math Help - Please help with this Q about simultaneous equations

  1. #1
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    Please help with this Q about simultaneous equations

    Hi I have to solve a really hard simultaneous equation and I don't know how to do it.

    Please note it has p1,p2,p3,q1,q2,q3. The numbers are subscripts.
    These all represent constant values. That is they are not variables.
    The two variables are x and y.

    1. x(q2+q3-2q1)-y(p2+p3-2p1)+(q1p2-p1q2)+(q1p3-q3p1)=0
    2. x(2q2-q1-q3)-y(2p2-p1-p3)+(p2q1-q2p1)+(p2q3-q2p3)=0

    I have tried to solve this by re-arranging then subbing in but this quickly gets out of hand as the subbed in equation is very long and
    it does not lead to the correct answer.

    Thanks in advance for replies.
    Last edited by James7361539; February 27th 2013 at 04:40 AM.
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  2. #2
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    Re: Please help with this Q about simultaneous equations

    Quote Originally Posted by James7361539 View Post
    Hi I have to solve a really hard simultaneous equation and I don't know how to do it.

    Please note it has p1,p2,p3,q1,q2,q3. The numbers are subscripts.
    These all represent constant values. That is they are not variables.
    The two variables are x and y.

    1. x(q2+q3-2q1)-y(p2+p3-2p1)+(q1p2-p1q2)+(q1p3-q3p1)
    2. x(2q2-q1-q3)-y(2p2-p1-p3)+(p2q1-q2p1)+(p2q3-q2p3)

    I have tried to solve this by re-arranging then subbing in but this quickly gets out of hand as the subbed in equation is very long and
    it does not lead to the correct answer.

    Thanks in advance for replies.
    Those aren't equations.
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  3. #3
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    Re: Please help with this Q about simultaneous equations

    Quote Originally Posted by a tutor View Post
    Those aren't equations.
    Sorry I forgot the =0 at the end of them
    I have edited my post now.
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  4. #4
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    Re: Please help with this Q about simultaneous equations

    So, essentially, you have Ax+ By= C and Dx+ Ey= F. Multiply the first equation by E, the second equation by B, and subtract:
    (AE- BD)x= CE- BF, x= (CE- BF)/(AE- BD).

    Multiply the first equation by D, the second equation by A, and subtract:
    (BD- AE)y= CD- AF, x= (CD- AF)/(BD- AE).

    Now replace A, B, C, D, E, and F with those complicated expressions.
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