f[x_,y_]:=10Sqrt[x^2+y^2]
g[x_,y_]:=4x-y+100
p0=Plot3D[{f[x,y],g[x,y]},{x,-20,20},{y,-20,20},PlotStyle->{{Red,Opacity[0.9]},{Blue,Opacity[0.9]}},Mesh->None,BoxRatios->{1,1,1}]

sol=Solve[f[x,y]==g[x,y],y]

p1=ParametricPlot3D[{{x,y/.sol[[1]],f[x,y/.sol[[1]]]},{x,y/.sol[[2]],f[x,y/.sol[[2]]]}},{x,-20,20},PlotStyle->{{AbsoluteThickness[10],Black}}]

Show[p0,p1]