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Solve the system of equations in `x,y and z` satisfying the following equations `x+[y]+{z}=3.1, y+[z]+{x}=4.3 and z+[x]+{y}=5.4` |
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Answer» 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` |
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