Solve the system of equation in `x , ya n dz` 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

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`