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Math Help - solve Matrices simultaneously

  1. #1
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    solve Matrices simultaneously

    4x+3y=2
    -x+7y=15

    \begin{bmatrix}{d11}{d12}&\\{d21}{d22}\end{bmatrix  } . \frac{x}{y}=\frac{b1}{b2}

    \frac{x}{y}=\begin{bmatrix}{A}\end{bmatrix}^{-1}\frac{b1}{b2}

    \begin{bmatrix}{4}&{3}\\{-1}&{7}\end{bmatrix}^{-1}\frac{2}{15}=\frac{x}{y}

    this is where im getin confused. do i need to find the inverse matrix then multiply out to get answer? im geting very big values

    many thanks
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  2. #2
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    Your method is correct. Proceed.
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  3. #3
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    However, writing \frac{x}{y} makes it look like a fraction!

    What you mean is
    \begin{bmatrix}4 & 3 \\ -1 & 7\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}= \begin{bmatrix} 2 \\ 15\end{bmatrix}

    so
    \begin{bmatrix}x \\ y\end{bmatrix}= \begin{bmatrix}4 & 3 \\ -1 & 7\end{bmatrix}^{-1}\begin{bmatrix} 2 \\ 16\end{bmatrix}

    Since the determinant of that is 4(7)- 3(-1)= 28+ 3= 31, you should NOT have very large numbers! You should have fractions with 31 in the denominator.
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