\(a-b=2\left(a+b\right)\)
\(\Leftrightarrow a-b=2a+2b\Leftrightarrow a=3b\)
\(\Leftrightarrow\frac{a}{b}=3\)
\(\Leftrightarrow\hept{\begin{cases}a+b=\frac{3}{2}\\a-b=3\end{cases}}\Leftrightarrow\hept{\begin{cases}a=\left(\frac{3}{2}+3\right):2=\frac{9}{4}\\b=\frac{9}{4}-3=\frac{-3}{4}\end{cases}}\)