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Thread: Solving Simultaneous Equations

  1. #1
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    Solving Simultaneous Equations

    Hi everyone, lately I have attempted to do a simple Simultaneous equations problem and it has stumped me for 2 days. Here is the problem:

     \frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5} (i)
     \frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4} (ii)

    I have attempted to solve this problem in 18 ways and they lead to different answer however non of them are correct (Correct answer: R=3, S=1/2 -Back of the book). Here is one of the attempts:

    (i)  20\left ( \frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5}\right )
     \therefore 12r+8-10s-5=44
     \therefore 12r-10s=44-8+5
     \therefore 12r-10s=41 (iii)

    (ii)  12\left ( \frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4} \right )
     \therefore 9+6r+20-4s=45
     \therefore 6r-4s=45-9-20
     \therefore 6r-4s=16 (iv)

    (iv)  2\left ( 6r-4s=16 \right )
     \therefore 12r-8s=32 (v)

    (iii - v)  -0-2s=9
     s=4.5

    If someone could explain to me how to do this, I would be really grateful because I'm starting to pull my hair out over this problem I think I'm doing something wrong with the numerators.
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  2. #2
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    Re: Solving Simultaneous Equations

    Quote Originally Posted by tracey3 View Post
    Hi everyone, lately I have attempted to do a simple Simultaneous equations problem and it has stumped me for 2 days. Here is the problem:

     \frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5} (i)
     \frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4} (ii)

    I have attempted to solve this problem in 18 ways and they lead to different answer however non of them are correct (Correct answer: R=3, S=1/2 -Back of the book). Here is one of the attempts:

    (i)  20\left ( \frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5}\right )
     \therefore 12r+8-10s\color{red}{+}5=44
     \therefore 12r-10s=44-8\color{red}{-}5
     \therefore 12r-10s=\color{red}{31} (iii)

    (ii)  12\left ( \frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4} \right )
     \therefore 9+6r+20-4s=45
     \therefore 6r-4s=45-9-20
     \therefore 6r-4s=16 (iv)
    correction made ... try again
    Thanks from tracey3
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  3. #3
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    Re: Solving Simultaneous Equations

     \frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5} (i)
     \frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4} (ii)

    Much easier if you start this way:
    (3r + 2) / 5 - 11 / 5 = (2s - 1) / 4 : (3r - 9) / 5 = (2s - 1) / 4

    Similarly with equation (ii).
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  4. #4
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    Re: Solving Simultaneous Equations

    Wow, it was such a simple mistake... Every time I try to come up with complex ways of solving this stuff, then its the simple things that catch you out.
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