$\left\{ \begin{array} { l } { x = 5y + 5 } \\ { 6 x - 4 y = 7 } \end{array} \right.$

## 共享

x-5y=5

x-5y=5,6x-4y=7

x-5y=5

x=5y+5

6\left(5y+5\right)-4y=7

30y+30-4y=7
6 乘上 5+5y。
26y+30=7

26y=-23

y=-\frac{23}{26}

x=5\left(-\frac{23}{26}\right)+5

x=-\frac{115}{26}+5
5 乘上 -\frac{23}{26}。
x=\frac{15}{26}

x=\frac{15}{26},y=-\frac{23}{26}

x-5y=5

x-5y=5,6x-4y=7

\left(\begin{matrix}1&-5\\6&-4\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}5\\7\end{matrix}\right)

inverse(\left(\begin{matrix}1&-5\\6&-4\end{matrix}\right))\left(\begin{matrix}1&-5\\6&-4\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&-5\\6&-4\end{matrix}\right))\left(\begin{matrix}5\\7\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&-5\\6&-4\end{matrix}\right))\left(\begin{matrix}5\\7\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&-5\\6&-4\end{matrix}\right))\left(\begin{matrix}5\\7\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{-4}{-4-\left(-5\times 6\right)}&-\frac{-5}{-4-\left(-5\times 6\right)}\\-\frac{6}{-4-\left(-5\times 6\right)}&\frac{1}{-4-\left(-5\times 6\right)}\end{matrix}\right)\left(\begin{matrix}5\\7\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{2}{13}&\frac{5}{26}\\-\frac{3}{13}&\frac{1}{26}\end{matrix}\right)\left(\begin{matrix}5\\7\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{2}{13}\times 5+\frac{5}{26}\times 7\\-\frac{3}{13}\times 5+\frac{1}{26}\times 7\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{15}{26}\\-\frac{23}{26}\end{matrix}\right)

x=\frac{15}{26},y=-\frac{23}{26}

x-5y=5

x-5y=5,6x-4y=7

6x+6\left(-5\right)y=6\times 5,6x-4y=7

6x-30y=30,6x-4y=7

6x-6x-30y+4y=30-7

-30y+4y=30-7

-26y=30-7

-26y=23

y=-\frac{23}{26}

6x-4\left(-\frac{23}{26}\right)=7

6x+\frac{46}{13}=7
-4 乘上 -\frac{23}{26}。
6x=\frac{45}{13}

x=\frac{15}{26}

x=\frac{15}{26},y=-\frac{23}{26}