Floor system of equations

$\begin{cases} x+ \lfloor y \rfloor+ \left \{ z \right \}=1.1\\ \lfloor x \rfloor+ \left \{ y \right \}+z=2.2 \\ \left \{ x \right \}+y+\lfloor z \rfloor=3.3 \end{cases}$

Find the solution to the system of equations and submit your answer as $x+y+z$ .

Notations :

• $\lfloor \cdot \rfloor$ denotes the floor function .
• $\lceil \cdot \rceil$ denotes the ceiling function .
• $\{ \cdot \}$ denotes the fractional part function .