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Maths Question - Simultaneous Equations

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  • 09-02-2012 10:06pm
    #1
    kayleigh01
    Registered Users Posts: 66 ✭✭


    a + b = 14

    a + bc = 16

    a + bc^2 = 19

    Solve for a, b and c.

    If you could help, I would be eternally grateful! :P


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    #2
    MathsManiac
    Registered Users Posts: 1,595 ✭✭✭MathsManiac


    Use the second one to write bc in terms of a. Sub that into the third one to get a quadratic in a. After you find the value(s) of a, you can then get b from the first equation and then c from the second.


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    #3
    kayleigh01
    Registered Users Posts: 66 ✭✭kayleigh01


    Ok, I understand that but I think the third one is (b x c^2) rather than (bc)^2 ?


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    #4
    finality
    Registered Users Posts: 1,763 ✭✭✭finality


    IMG_20120209_214206.jpg

    enjoy!


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    #5
    kayleigh01
    Registered Users Posts: 66 ✭✭kayleigh01


    Thank you so so so much! :)


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    #6
    finality
    Registered Users Posts: 1,763 ✭✭✭finality


    kayleigh01 wrote: »
    Thank you so so so much! :)

    no problem, I just hope it's right...it'd be pretty embarrassing otherwise :P


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    #7
    Shalashaska
    Registered Users Posts: 56 ✭✭Shalashaska


    finality wrote: »
    no problem, I just hope it's right...it'd be pretty embarrassing otherwise :P

    I was about to save the day there :D. It's right.


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    #8
    MathsManiac
    Registered Users Posts: 1,595 ✭✭✭MathsManiac


    Sorry for the misinterpretation.


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    #9
    siobhanod93
    Registered Users Posts: 179 ✭✭siobhanod93


    :eek::eek: Spoiler:
    That came up on the DEB mock


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    #10
    finality
    Registered Users Posts: 1,763 ✭✭✭finality


    siobhanod93 wrote: »
    :eek::eek: Spoiler:
    That came up on the DEB mock
    indeed. I'm hoping I actually got it right in the exam. :L


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    #11
    Joza
    Registered Users Posts: 58 ✭✭Joza


    The important thing is, do you know how to do the question?!

    You have three unknown quantities, a, b and c. You then have three equations.

    You just rearrange one of them ( it doesn't matter which one) so that you have just one of the quantities on one side, and nothing else on that side either.

    Say you have a = ... then you plug that value of a into the next equation (which no longer has a in it now) and solve for say b or c.

    Then plug that value into the next. Once you get an actual number for one of them, start plugging that number back in to the equations and work out the value of the numbers for the rest.

    I hope that helps!!


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    #12
    Mwalimu
    Registered Users Posts: 42 ✭Mwalimu


    Equation 2 - Equation 1 gives bc - b = 2 (call this Eqn 4)
    Equation 3 - Equation 2 gives bc^2 - bc = 3 or c(bc - b) = 3 by factoring (Call this Eqn 5)
    Now use Eqn 4 in Eqn 5 to get 2c = 3 and so c = 3/2
    Sub this into Eqn 4 and get b = 4
    Sub that into Eqn 1 to get a = 10
    ;)


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