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Math Help - Simultaneous equations in matrices

  1. #1
    Newbie
    Joined
    May 2009
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    1

    Exclamation Simultaneous equations in matrices

    Hi

    I'm having a little problem solving simultaneous equations in matrices.

    2b + t = 14
    5b + 5t = 40

    [2 1] [b] [14]
    [5 5] [t] [40]

    1
    _____
    ad-bc

    =

    1
    _____
    (2x5) - (1x5) = 5

    [5 -1] [14]
    [-5 2] [40]

    Then how do I go from there to get:

    x(b) = 6
    y(t) = 2

    I just don't know how to do it
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  2. #2
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    What is that you're doing? Are you supposed to solve by using some particular method? Are you maybe using Cramer's Rule...?

    Thank you!
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  3. #3
    Super Member Showcase_22's Avatar
    Joined
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    \begin{pmatrix}<br />
2&1\\<br />
5&5<br />
\end{pmatrix} \begin{pmatrix}<br />
b\\<br />
t<br />
\end{pmatrix}=\begin{pmatrix}<br />
14\\<br />
40<br />
\end{pmatrix}

    \begin{pmatrix}<br />
b\\<br />
t<br />
\end{pmatrix}=\frac{1}{5} \begin{pmatrix}<br />
5&{-1}\\<br />
{-5}&{2}<br />
\end{pmatrix}\begin{pmatrix}<br />
14\\<br />
40<br />
\end{pmatrix}

    can you solve it from there?
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