\[\left\{ \begin{matrix} a + b = 2\ \ | \cdot ( - 2) \\ 5a + 2b = 3\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} - 2a - 2b = - 4\ \ (1) \\ 5a + 2b = 3\ \ \ \ \ \ \ \ \ (2) \\ \end{matrix} \right.\ \]
\[(1) + (2) \Longrightarrow 3a = - 1\]
\[\left\{ \begin{matrix} 3a = - 1\ \ \\ a + b = 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 3a = - 1\ \ \\ b = 2 - a \\ \end{matrix} \right.\ \]