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Thread: Faster way to work out multiples

  1. #1
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    Faster way to work out multiples

    Hi all, my fractions are not great to be honest but here is my question.

    Using addition, solve for a and b:

    $\displaystyle 4a-6b=15$
    $\displaystyle 6a-4b=10$

    So I find a common multiple of b, I choose to use 24.

    $\displaystyle 16a-24b=60$
    $\displaystyle 36a-24b=60$

    Now I go ahead and do the addition:

    $\displaystyle 16a-24b=60$
    $\displaystyle -36a+24b=-60$

    I'm left with: $\displaystyle -20a=0 == a=0$

    Is this correct so far? If so then I plug the answer back into the equation and get:

    $\displaystyle 4-6b=15$

    I only know from using a website that $\displaystyle b=-\frac{5}{2}$

    My question is I just don't know how to go about finding the correct fraction, is there a simple method?
    Last edited by uperkurk; Mar 18th 2013 at 04:37 PM.
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  2. #2
    Junior Member Kanwar245's Avatar
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    Re: Faster way to work out multiples

    After you've found your answers plug them back in the two equations and see if LHS = RHS
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    Re: Faster way to work out multiples

    I don't know what LHS = RHS means. Could you elaborate?
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    Junior Member Kanwar245's Avatar
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    Re: Faster way to work out multiples

    LHS means left hand side, RHS means right hand side
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    Re: Faster way to work out multiples

    But my question was with regards to finding the quick way to the correct fraction
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    Senior Member Paze's Avatar
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    Re: Faster way to work out multiples

    Hi Uperkurk.

    Your method is correct.

    Your answer also seems to be correct. You are left with $\displaystyle a=0$ So by plugging that into either one of your equations (I'm choosing the first one for my example), you get $\displaystyle 4\cdot 0-6b\right)=15$ It seems that by solving this equation you get $\displaystyle b=\frac{-5}{2}$ which is harmonious with the answer.

    For a more in-depth view on how to solve the equation

    $\displaystyle \\4\cdot 0-6b=15\\\\0-6b=15\\\\-6b=15\\\\b=\frac{15}{-6}\\\\b=-\frac{5}{2}$

    Does this clear it up for you?
    Last edited by Paze; Mar 18th 2013 at 05:55 PM.
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    Re: Faster way to work out multiples

    Quote Originally Posted by Paze View Post
    Hi Uperkurk.

    Your method is correct.

    Your answer also seems to be correct. You are left with $\displaystyle a=0$ So by plugging that into either one of your equations (I'm choosing the first one for my example), you get $\displaystyle 4\cdot 0-6b\right)=15$ It seems that by solving this equation you get $\displaystyle b=\frac{-5}{2}$ which is harmonious with the answer.

    For a more in-depth view on how to solve the equation

    $\displaystyle \\4\cdot 0-6b=15\\\\0-6b=15\\\\-6b=15\\\\b=\frac{15}{-6}\\\\b=-\frac{5}{2}$

    Does this clear it up for you?
    Perfect, thank you.
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