$\estwo{8 x + 2 y = 46}{7 x + 3 y = 47}$

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8x+2y=46,7x+3y=47

8x+2y=46

8x=-2y+46

x=\frac{1}{8}\left(-2y+46\right)

x=-\frac{1}{4}y+\frac{23}{4}

7\left(-\frac{1}{4}y+\frac{23}{4}\right)+3y=47

-\frac{7}{4}y+\frac{161}{4}+3y=47

\frac{5}{4}y+\frac{161}{4}=47

\frac{5}{4}y=\frac{27}{4}

y=\frac{27}{5}

x=-\frac{1}{4}\times \left(\frac{27}{5}\right)+\frac{23}{4}

x=-\frac{27}{20}+\frac{23}{4}
-\frac{1}{4} 乘以 \frac{27}{5} 的计算方法是，将两数分子与分子相乘得到分子，分母与分母相乘得到分母。如果可能，将所得分数化为最简分数。
x=\frac{22}{5}

x=\frac{22}{5},y=\frac{27}{5}

8x+2y=46,7x+3y=47

\left(\begin{matrix}8&2\\7&3\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}46\\47\end{matrix}\right)

inverse(\left(\begin{matrix}8&2\\7&3\end{matrix}\right))\left(\begin{matrix}8&2\\7&3\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}8&2\\7&3\end{matrix}\right))\left(\begin{matrix}46\\47\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}8&2\\7&3\end{matrix}\right))\left(\begin{matrix}46\\47\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}8&2\\7&3\end{matrix}\right))\left(\begin{matrix}46\\47\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{3}{8\times 3-2\times 7}&-\frac{2}{8\times 3-2\times 7}\\-\frac{7}{8\times 3-2\times 7}&\frac{8}{8\times 3-2\times 7}\end{matrix}\right)\left(\begin{matrix}46\\47\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{3}{10}&-\frac{1}{5}\\-\frac{7}{10}&\frac{4}{5}\end{matrix}\right)\left(\begin{matrix}46\\47\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{3}{10}\times 46-\frac{1}{5}\times 47\\-\frac{7}{10}\times 46+\frac{4}{5}\times 47\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{22}{5}\\\frac{27}{5}\end{matrix}\right)

x=\frac{22}{5},y=\frac{27}{5}

8x+2y=46,7x+3y=47

7\times 8x+7\times 2y=7\times 46,8\times 7x+8\times 3y=8\times 47

56x+14y=322,56x+24y=376

56x-56x+14y-24y=322-376

14y-24y=322-376

-10y=322-376

-10y=-54

y=\frac{27}{5}

7x+3\times \left(\frac{27}{5}\right)=47

7x+\frac{81}{5}=47

7x=\frac{154}{5}

x=\frac{22}{5}

x=\frac{22}{5},y=\frac{27}{5}