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Math Help - Simultaneous Equations

  1. #1
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    Thumbs up Simultaneous Equations

    HI Guys,

    Can any body solve these simultaneous equations:

    2a + 3(a-b) = 7
    4b + 3(b-a) = 1

    If anybody could show me how to do these that would be great !!

    Thanks!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sparkdog View Post
    HI Guys,

    Can any body solve these simultaneous equations:

    2a + 3(a-b) = 7
    4b + 3(b-a) = 1

    If anybody could show me how to do these that would be great !!

    Thanks!
    Well start by simplifying:
    2a + 3(a - b) = 7 \implies 5a - 3b = 7
    and
    4b + 3(b - a) = 1 \implies -3a + 7b = 1

    The way I typically solve these is by substitution. For example, solve the bottom equation for a:
    a = \frac{7b - 1}{3}

    Then insert this value for a in to the top equation:
    \frac{5}{3} \cdot (7b - 1) - 3b = 7

    Now solve this for b and then put that into the "a" equation above.

    -Dan
    Last edited by topsquark; January 5th 2008 at 08:39 AM.
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  3. #3
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    Thanks for your help Dan, that great.

    Im not sure if you have simplified the 2nd equation correct tho.

    The second equation was 4b + 3(b-a) = 1

    you had got it as 4b + (3b - a) = 1.

    Sorry !
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sparkdog View Post
    Thanks for your help Dan, that great.

    Im not sure if you have simplified the 2nd equation correct tho.

    The second equation was 4b + 3(b-a) = 1

    you had got it as 4b + (3b - a) = 1.

    Sorry !
    Whoops! A typo that I carried through. Thanks for the catch.

    -Dan
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