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adding subset of interpolating function from a system of ODE


hello group. 

Please consider the lorenz system for example. 

In[2]:=
solution=NDSolve[{Derivative[1][x][t]\[Equal]-y[t]-z[t],x[0]\[Equal]-0.04,
        Derivative[1][y][t]\[Equal]x[t]+0.425*y[t],y[0]\[Equal]-0.3,
        Derivative[1][z][t]\[Equal]2-(4-x[t])*z[t],z[0]\[Equal]0.52},{x[t],
        y[t],z[t]},{t,0,25}];

ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.solution],{t,0,25},
    PlotPoints -> 1000,PlotRange ->All];

above shows a parametric plot of x, y and z. 

but let's say for some reason I want to plot the following..

x+y vs time
x+z vs  y

how do I achieve this?  is this possible in mathematica? 

as always any and all thoughts are appreciated. 

thank you all in advance

sean


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