Saddles and Rational Expectations. Language barrier preventing me to solve this exercise
$\newcommand{\vect}[1]{{\bf #1}}$

Note that you can write the system in the form

$$
\dot{\vect{x}} = A \vect{x} + \vect{b}
$$

where 

$$
\vect{x} = \left(\begin{array}{c} x \\ y\end{array}\right), ~~~~ A = \left(\begin{array}{cc} 1 &amp; 1 \\ 2 &amp; -1\end{array}\right), ~~~~~ \vect{b} = \left(\begin{array}{c} 1 \\ 5\end{array}\right)
$$

A fixed point $\vect{x}^*$ is a point for which $A\vect{x}^* + \vect{b} = 0$, which in this case is 

$$
\vect{x}^* = \left(\begin{array}{c} -2 \\ 1\end{array}\right)
$$

Now define the variable

$$
\vect{z} = \vect{x} - \vect{x}^*
$$

and note that 

$$
\dot{\vect{z}} = \dot{\vect{x}} = A\vect{x} + \vect{b} = A\vect{x} - A\vect{x}^* = A(\vect{x} - \vect{x}^*) = A\vect{z}
$$

That is,

$$
\dot{\vect{z}} = A \vect{z}
$$

What you need to do now is to find the eigen-decomposition of $A$