$\estwo{\fraction{3}{2} a + b = 1}{a + \fraction{b}{2} = 7}$

## 共享

\frac{3}{2}a+b=1,a+\frac{1}{2}b=7

\frac{3}{2}a+b=1

\frac{3}{2}a=-b+1

a=\frac{2}{3}\left(-b+1\right)

a=-\frac{2}{3}b+\frac{2}{3}

-\frac{2}{3}b+\frac{2}{3}+\frac{1}{2}b=7

-\frac{1}{6}b+\frac{2}{3}=7

-\frac{1}{6}b=\frac{19}{3}

b=-38

a=-\frac{2}{3}\left(-38\right)+\frac{2}{3}

a=\frac{76+2}{3}

a=26

a=26,b=-38

\frac{3}{2}a+b=1,a+\frac{1}{2}b=7

\left(\begin{matrix}\frac{3}{2}&1\\1&\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}1\\7\end{matrix}\right)

inverse(\left(\begin{matrix}\frac{3}{2}&1\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}\frac{3}{2}&1\\1&\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}a\\b\end{matrix}\right)=inverse(\left(\begin{matrix}\frac{3}{2}&1\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}1\\7\end{matrix}\right)

\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}a\\b\end{matrix}\right)=inverse(\left(\begin{matrix}\frac{3}{2}&1\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}1\\7\end{matrix}\right)

\left(\begin{matrix}a\\b\end{matrix}\right)=inverse(\left(\begin{matrix}\frac{3}{2}&1\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}1\\7\end{matrix}\right)

\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}\frac{\frac{1}{2}}{\frac{3}{2}\times \left(\frac{1}{2}\right)-1}&-\frac{1}{\frac{3}{2}\times \left(\frac{1}{2}\right)-1}\\-\frac{1}{\frac{3}{2}\times \left(\frac{1}{2}\right)-1}&\frac{\frac{3}{2}}{\frac{3}{2}\times \left(\frac{1}{2}\right)-1}\end{matrix}\right)\left(\begin{matrix}1\\7\end{matrix}\right)

\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}-2&4\\4&-6\end{matrix}\right)\left(\begin{matrix}1\\7\end{matrix}\right)

\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}-2+4\times 7\\4-6\times 7\end{matrix}\right)

\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}26\\-38\end{matrix}\right)

a=26,b=-38

\frac{3}{2}a+b=1,a+\frac{1}{2}b=7

\frac{3}{2}a+b=1,\frac{3}{2}a+\frac{3}{2}\times \left(\frac{1}{2}\right)b=\frac{3}{2}\times 7

\frac{3}{2}a+b=1,\frac{3}{2}a+\frac{3}{4}b=\frac{21}{2}

\frac{3}{2}a-\frac{3}{2}a+b-\frac{3}{4}b=1-\frac{21}{2}

b-\frac{3}{4}b=1-\frac{21}{2}

\frac{1}{4}b=1-\frac{21}{2}

\frac{1}{4}b=-\frac{19}{2}

b=-38

a+\frac{1}{2}\left(-38\right)=7

a-19=7

a=26

a=26,b=-38