Solve the system of equations in x, y, and z satisfying the following equations:

$x+[y] + \{z\} = 3.1$

$\{x\} +y+[z] = 4.3$

$[x]+ \{y\} +z = 5.4$

(where [.] denotes the greatest integer function and {.} denotes the fractional part function.)

$x = 2, y = 1.3, z = 3.1$

Adding all the three equations, we get

$2(x + y + z) = 12.8$ or $x + y + z = 6.4$  ...... (1)

Adding the first two equations, we get

$x+y+z+ [y] + \{x\} = 7.4$ .......(2)

Adding the second and third equations, we get

$x+y+z+ [z] + \{y\} = 9.7$  ......(3)

Adding the first and third equations, we get 

$x+y+z+ [x] + \{z\} = 8.5$   ....(4)

From (1) and (2), $[y] + \{x\} = 1$.

From (1) and (3), $[z] + \{y\} = 3.3$.

From (1) and (4), $[x] + \{z\} = 2.1$. So,

$[x] = 2, [y]= 1, [z] = 3,$

$\{x\} = 0, \{y\} = 0.3$, and $\{z\} = 0.1$

$∴x = 2, y = 1.3, z = 3.1$