Solve the following system of equations:

$$
\begin{aligned}
& x+[y]+\{z\}=1.1 \\
& \{x\}+y+[z]=2.2 \\
& {[x]+\{y\}+z=3.3}
\end{aligned}
$$

where $[x]$ denotes the greatest integer not greater than $x$, and $\{x\}=x-[x]$.