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Question Number 37084 by Rio Mike last updated on 08/Jun/18

$$solveusingmatrixmethod$$$$x-y=4$$$$2x-3y=5$$

Commented by math khazana by abdo last updated on 09/Jun/18

$$\left(s\right)\iff \left(\begin{array}{c}1-1\\ 2-3\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}4\\ 5\end{array}\right)\iff A.\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}4\\ 5\end{array}\right)$$$$detA=-1\ne 0\Rightarrow \left(\begin{array}{c}x\\ y\end{array}\right)=A^{-1}.\left(\begin{array}{c}4\\ 5\end{array}\right)$$$$A^{-1}=\frac{t\left(comA\right)}{detA}withcomA={(-1)}^{i+j}{A}_{ij}$$$$=\left(\begin{array}{c}{a}_{11}{a}_{12}\\ a_{21}{a}_{22}\end{array}\right)=\left(\begin{array}{c}-3-2\\ 11\end{array}\right)and$$$$t\left(comA\right)=\left(\begin{array}{c}-31\\ -21\end{array}\right)\Rightarrow A^{-1}=\left(\begin{array}{c}3-1\\ 2-1\end{array}\right)$$$$\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}3-1\\ 2-1\end{array}\right)\left(\begin{array}{c}4\\ 5\end{array}\right)=\left(\begin{array}{c}7\\ 3\end{array}\right)\Rightarrow x=7andy=3$$

Commented by math khazana by abdo last updated on 09/Jun/18

$$thismethodisgeneralfornunknown\left(x_i\right)if$$$$thematrixAisinversible.$$

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