solution=NDSolve[
        {
         x'[t]==  x[t]+y[t]-t,
         y'[t]==  x[t]-y[t]+t ,
         z'[t]==    z[t]+x[t],
         x[0]==0,
         y[0]==0,
         z[0]==0
          },
         {x,y,z},
         {t,0,10}]

<<Graphics`Graphics`

ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/. solution],
                {t,0,10},
                AxesLabel->{"x","y","z"}]

Plot[Evaluate[x[t]/. solution],{t,0,10},
AxesLabel->{"t","x(t)"}]

Plot[Evaluate[y[t]/. solution],{t,0,10},
        AxesLabel->{"t","y(t)"}]

Plot[Evaluate[z[t]/. solution],{t,0,10},
     AxesLabel->{"t","z(t)"}]