The system of equations:
[tex]\begin{gathered} 6x+7y=14 \\ 7x+8y=27 \end{gathered}[/tex]
can be written as:
[tex]\begin{bmatrix}6 & 7 \\ 7 & 8\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}=\begin{bmatrix}14 \\ 27\end{bmatrix}[/tex]
To find the solution we need to find the inverse matrix of the coefficients matrix. For a two by two matrix the inverse is given as:
[tex]\frac{1}{\mbox{det }A}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}[/tex]
Then in this case the inverse matrix is
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