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x+y=9,4x+5y=39

x+y=9

x=-y+9

4\left(-y+9\right)+5y=39

-4y+36+5y=39

y+36=39

y=3

x=-3+9

x=6

x=6,y=3

x+y=9,4x+5y=39

\left(\begin{matrix}1&1\\4&5\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}9\\39\end{matrix}\right)

inverse(\left(\begin{matrix}1&1\\4&5\end{matrix}\right))\left(\begin{matrix}1&1\\4&5\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\4&5\end{matrix}\right))\left(\begin{matrix}9\\39\end{matrix}\right)

\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\4&5\end{matrix}\right))\left(\begin{matrix}9\\39\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\4&5\end{matrix}\right))\left(\begin{matrix}9\\39\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{5}{5-4}&-\frac{1}{5-4}\\-\frac{4}{5-4}&\frac{1}{5-4}\end{matrix}\right)\left(\begin{matrix}9\\39\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}5&-1\\-4&1\end{matrix}\right)\left(\begin{matrix}9\\39\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}5\times 9-39\\-4\times 9+39\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}6\\3\end{matrix}\right)

x=6,y=3

x+y=9,4x+5y=39

4x+4y=4\times 9,4x+5y=39

4x+4y=36,4x+5y=39

4x-4x+4y-5y=36-39

4y-5y=36-39

-y=36-39

-y=-3

y=3

4x+5\times 3=39

4x+15=39

4x=24

x=6

x=6,y=3