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Question Number 10621 by ketto last updated on 20/Feb/17

Answered by mrW1 last updated on 20/Feb/17

$$xboysandygirls$$$$x-y=10\left(i\right)$$$$x=2(y+1)or$$$$x-2y=2\left(ii\right)$$$$$$$$\left(\begin{array}{cc}1& -1\\ 1& -2\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}10\\ 2\end{array}\right)$$$$A=\left(\begin{array}{cc}1& -1\\ 1& -2\end{array}\right)$$$$\mid A\mid =\left|\begin{array}{cc}1& -1\\ 1& -2\end{array}\right|=-2+1=-1$$$$A^{-1}=\frac{1}{-1}\left(\begin{array}{cc}-2& 1\\ -1& 1\end{array}\right)=\left(\begin{array}{cc}2& -1\\ 1& -1\end{array}\right)$$$$$$$$\left(\begin{array}{c}x\\ y\end{array}\right)=A^{-1}\left(\begin{array}{c}10\\ 2\end{array}\right)=\left(\begin{array}{cc}2& -1\\ 1& -1\end{array}\right)\left(\begin{array}{c}10\\ 2\end{array}\right)=\left(\begin{array}{c}18\\ 8\end{array}\right)$$$$$$$$\Rightarrow 18boysand8girls$$

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