Solve the system of equation in `x , y andz` 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.)

Explanation

`:'[x]+{x}=x,[y]+{y}=z` and `[z]+{z}=z`
On adding all the three equations we get
`2(x+y+z)=128`
`impliesx+y+z=6.4`……i
Now adding first two equations we get
`x+y+z+[y]+{x}=7.4`
`implies6.4+[y]+{x}=7.4`[from Eq. (i) ]
`implies[y]+{x}=1`
`:.[y]=1` and `{x}=0`..........ii
On adding last two equations, we get
`x+y=z+{y}+[z]=9.7`
`{y}+[z]=3.3` [from Eq. (ii)]
`:.[z]=3` and `{y}=0.3`.............iii
On adding first and last equations we get
`x+y+z+[x]+{z}=8.5`
`implies[x]+{z}=2.1` [from Eq. (i) ]
`:.[x]=2,{z}=0.1`.....iv
From Eqs i, ii and iii we get
`x=[x]+{x}=2+0=2`
`y=[y]+{y}=1+0.3=1.3`
and `z=[z]+{z}=3+0.1=3.1`