Manipulate[Show[{
Graphics3D[{{Opacity[.9],
If[p1,Polygon[{{-5,-5,0},{-5,5,0},{5,5,0},{5,-5,0}}],Nothing],
If[p2,Polygon[{{0,-5,-5},{0,-5,5},{0,5,5},{0,5,-5}}],Nothing],
If[p3,Polygon[{{-10,-5,-5},{-10,-5,5},{10,5,5},{10,5,-5}}],Nothing]}},
PlotRange->3,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{"x","y","z"},AxesStyle->Black],
If[p4,Plot3D[2-x-2y,{x,-3,3},{y,-3,3},PlotStyle->Gray,Mesh->None],Nothing]
}],{{p1,True},{True,False}},{{p2,False},{True,False}},{{p3,False},{True,False}},{{p4,False},{True,False}}]

RegionPlot3D[z≥0&&x≥0&&2y≥x&&z≤2-x-2y,{x,-0.1,1},{y,-0.1,1.1},{z,-0.1,2},PlotPoints->100,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{"x","y","z"},AxesStyle->Black,Mesh->None,PlotStyle->Magenta]

Manipulate[Show[{
Graphics3D[{{Opacity[.5],
If[p1,Polygon[{{-5,-5,0},{-5,5,0},{5,5,0},{5,-5,0}}],Nothing],
If[p2,Polygon[{{0,-5,-5},{0,-5,5},{0,5,5},{0,5,-5}}],Nothing],
If[p3,Polygon[{{-10,-5,-5},{-10,-5,5},{10,5,5},{10,5,-5}}],Nothing]}},
PlotRange->3,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{"x","y","z"},AxesStyle->Black],
If[p4,Plot3D[2-x-2y,{x,-3,3},{y,-3,3},PlotStyle->{Gray,Opacity[.5]},Mesh->None],Nothing],
RegionPlot3D[z≥0&&x≥0&&2y≥x&&z≤2-x-2y,{x,-0.1,1},{y,-0.1,1.1},{z,-0.1,2},PlotPoints->100,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{"x","y","z"},AxesStyle->Black,Mesh->None,PlotStyle->Magenta]
}],{{p1,True},{True,False}},{{p2,False},{True,False}},{{p3,False},{True,False}},{{p4,False},{True,False}}]