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Solve simultaneus Equation

  1. Jun 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve for a and b

    [itex]
    \frac{a}{3}+\frac{b}{4}=1[/itex]

    2. Relevant equations



    3. The attempt at a solution

    My Teacher went straight from:

    [itex]\frac{a}{3}+\frac{b}{4}=1[/itex]

    To

    [itex] a = 2\left(1-\frac{b}{3}\right)[/itex]

    I was wondering If there is a nice trick to get to that step so quickly.

    When I try the first thing I do is:

    [itex]\frac{a}{3} = 1 - \left(\frac{b}{4}\right)[/itex]

    than:

    [itex]a = \left[1 - \left(\frac{b}{4}\right)\right]\times 3[/itex]

    and I end up with

    [itex]a=\frac{-3(b-4)}{4}[/itex]

    So mine seems alot more messy and I'm not sure how he gets to:

    [itex] a = 2\left(1-\frac{b}{3}\right)[/itex]

    Regards
     
  2. jcsd
  3. Jun 10, 2009 #2

    statdad

    User Avatar
    Homework Helper

    Your answer seems to be the correct one - I'm not sure what your teacher was thinking (unless there is a part of the problem you didn't provide).
    One more question: since you ask about solving for [tex] a [/tex] and [tex] b [/tex], is there another equation? A single equation is not
    a set of simultaneous equations.
     
  4. Jun 10, 2009 #3

    Mark44

    Staff: Mentor

    Since you and your teacher both solve the same equation for a and got different solutions, and the two are obviously different, you can easily determine that one of them (at least) is incorrect. Just replace a in the original equation by your expression for a. If you get an identically true statement, then your solution is correct. Similarly, if you replace a by the expression your teacher shows, then his/her solution is correct.
     
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