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    • Thread Starter

    Hello. I'm not primarily a mathematician, and I expect I'm missing something quite obvious/easy (I haven't done linear equations in a very long time), but I was looking over this linear equation question and I'm not sure how to work it out.

    6b + 9m = £23.40
    8b + 5m = £21.40

    Question: Find b and m.

    An explanation of how to calculate this would be appreciate.

    Many thanks!

    From the first one:
    6b = 23.4 - 9m
    b= (23.4-9m)/6

    Suc into second

    8(23.4 - 9m)/6 + 5m = 21.4

    The solve using our good friend a calculator by getting m = something and sub in your value for m into one of the orginal equations to get b
    • PS Helper

    PS Helper
    You need to try and multiply the equations by something so that, if you take one away from the other, one of the variables (b or m) will vanish.

    In this case, it would probably be easiest to make the b vanish (because they share a common factor of 2). If you multiply the first equation by 4 and the second equation by 3, you get:
    24b + 36m = £93.60
    24b + 15m = £64.20

    You'll notice that both of the bs are multiplied by 24, so if you subtract the second equation from the first equation, the "24b" terms disappear, and you're left with:

    36m - 16m = £29.40

    And hence

    20m = £29.40

    You can then solve this for m, and now that you've got your value for m you can substitute back into either of the original equations to solve for b.

    Also you might want to check what I did, I'm in a hurry so I did it all in my head so some of the numbers might be wrong :p:
    • Thread Starter

    Thank you, very helpful explanations.

    It makes sense! Yay! xd
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