$\left\{ \begin{array} { l } { 2 x + y = 3 } \\ { x - y = 1 } \end{array} \right.$

## 共享

2x+y=3,x-y=1

2x+y=3

2x=-y+3

x=\frac{1}{2}\left(-y+3\right)

x=-\frac{1}{2}y+\frac{3}{2}

-\frac{1}{2}y+\frac{3}{2}-y=1

-\frac{3}{2}y+\frac{3}{2}=1

-\frac{3}{2}y=-\frac{1}{2}

y=\frac{1}{3}

x=-\frac{1}{2}\times \left(\frac{1}{3}\right)+\frac{3}{2}

x=-\frac{1}{6}+\frac{3}{2}
-\frac{1}{2} 乘以 \frac{1}{3} 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{4}{3}

x=\frac{4}{3},y=\frac{1}{3}

2x+y=3,x-y=1

\left(\begin{matrix}2&1\\1&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}3\\1\end{matrix}\right)

inverse(\left(\begin{matrix}2&1\\1&-1\end{matrix}\right))\left(\begin{matrix}2&1\\1&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&1\\1&-1\end{matrix}\right))\left(\begin{matrix}3\\1\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}2&1\\1&-1\end{matrix}\right))\left(\begin{matrix}3\\1\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&1\\1&-1\end{matrix}\right))\left(\begin{matrix}3\\1\end{matrix}\right)

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

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

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

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{4}{3}\\\frac{1}{3}\end{matrix}\right)

x=\frac{4}{3},y=\frac{1}{3}

2x+y=3,x-y=1

2x+y=3,2x+2\left(-1\right)y=2

2x+y=3,2x-2y=2

2x-2x+y+2y=3-2

y+2y=3-2

3y=3-2

3y=1

y=\frac{1}{3}

x-\frac{1}{3}=1

x=\frac{4}{3}

x=\frac{4}{3},y=\frac{1}{3}