\[\boxed{\text{426\ (426).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\left\{ \begin{matrix} x + y = a + 1\ \ \\ 3x - y = a - 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = a + 1 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x - (a + 1 - x) = a - 1 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = a + 1 - x \\ 4x = 2a\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = a + 1 - 0,5a \\ x = 0,5a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 0,5a + 1 \\ x = 0,5a\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[так\ как\ x > 0\ \ и\ \ y > 0 \Longrightarrow a > 0.\]
\[Ответ:при\ a > 0.\]