\[\left\{ \begin{matrix} 2a - 3b = 1\ \ | \cdot ( - 2) \\ 4a + 2b = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} - 4a + 6b = - 2\ \ (1) \\ 4a + 2b = 3\ \ \ \ \ \ \ \ \ (2) \\ \end{matrix} \right.\ \]
\[(1) + (2) \Longrightarrow 8b = 1\]
\[\left\{ \begin{matrix} 8b = 1\ \ \ \ \ \ \ \ \ \ \\ 2a - 3b = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 8b = 1\ \ \ \ \ \ \ \ \ \ \ \\ 2a = 1 + 3b \\ \end{matrix} \right.\ \]