$解:解方程組\begin{cases}{x+y=\frac{4}{3}}\\{x-y=\frac{6}{5}}\end{cases},得\begin{cases}{x=\frac{19}{15}}\\{y=\frac{1}{15}}\end{cases}$
$即原方程組的解為\begin{cases}{x=\frac{19}{15}}\\{y=\frac{1}{15}}\end{cases}$
$將\begin{cases}{x+y=\frac{4}{3}}\\{x-y=\frac{6}{5}}\end{cases}代入原方程組$
$得\begin{cases}{\frac{1}{3}b-\frac{12}{5}a=-\frac{2}{15}}\\{2a-b=-\frac{4}{3}}\end{cases},解得\begin{cases}{a=\frac{1}{3}}\\{b=2}\end{cases}$