In[]:=
ℛ
1
=x^2+y^2==1&&x==y​​rng1={{-a,a},{-a,a}}/.a->3/2;​​Region[ImplicitRegion[
ℛ
1
,{x,y}],PlotRangerng1,Axes->True,ImagePadding->All,PlotLabel->ToString[{x,y}/.Solve[
ℛ
1
,{x,y}],StandardForm]]
Out[]=
2
x
+
2
y
1&&xy
Out[]=
In[]:=
ℛ
2
=2x+3y-5z==1&&3x-4y+7z3;​​rng2={{-a,a},{-a,a},{-a,a}}/.a->2;​​Region[ImplicitRegion[
ℛ
2
,{x,y,z}],PlotRangerng2,Axes->True,AxesLabel->{x,y,z},AxesOrigin->{0,0,0},ImagePadding->All,PlotLabel->ToString[{x,y,z}/.Solve[
ℛ
2
,{x,y,z}],StandardForm]]
Out[]=
In[]:=
ℛ
3
=xyz^2-x&&xyz2&&x^2+y^2+z^2≤5;​​rng3={{-a,a},{-a,a},{-a,a}}/.a->2;​​Assuming[{x,y,z}∈Reals,Region[ImplicitRegion[
ℛ
3
,{x,y,z}],PlotRangerng3,Axes->True,AxesLabel->{x,y,z},AxesOrigin->{0,0,0},ImagePadding->All,PlotLabel->ToString[{x,y,z}/.FullSimplify[Solve[
ℛ
3
,{x,y,z}]],StandardForm]]]
Out[]=
In[]:=
ℛ
4
=x+y+z==1&&x+2y-z==3;​​rng4={{-a,a},{-a,a},{-a,a}}/.a->2;​​Assuming[{x,y,z}∈Reals,Region[ImplicitRegion[
ℛ
4
,{x,y,z}],PlotRangerng4,Axes->True,AxesLabel->{x,y,z},AxesOrigin->{0,0,0},ImagePadding->All,PlotLabel->ToString[{x,y,z}/.FullSimplify[Solve[
ℛ
4
,{x,y,z}]],StandardForm]]]
Out[]=
ℛ
5
=Sqrt[x+2y]-3x+4y≥5&&x+y^(1/3)1;​​rng5={{-1,1},{-1,a}}/.a->3;​​Region[ImplicitRegion[
ℛ
5
,{x,y}],PlotRangerng5,Axes->True,ImagePadding->All,PlotLabel->ToString[{x,y}/.Solve[
ℛ
5
,{x,y}],StandardForm]]
Out[]=
-3x+4y+
x+2y
≥5&&x+
1/3
y
1
Out[]=
In[]:=
ℛ
6
=E^xy^3+Log[x]y1&&xy+E^x/x≥2;​​rng6={{-a,a},{-a,a}}/.a->5;​​Region[ImplicitRegion[
ℛ
6
,{x,y}],PlotRangerng6,Axes->True,ImagePadding->All]
RegionPlot
:ImplicitRegionLog[x]y+
x

3
y
1&&
x

x
+xy≥2,{x,y} cannot be automatically discretized.
RegionPlot
:ImplicitRegionLog[x]y+
x

3
y
1&&
x

x
+xy≥2,{x,y} is not a valid region to plot.
RegionPlot
:ImplicitRegionLog[x]y+
x

3
y
1&&
x

x
+xy≥2,{x,y} cannot be automatically discretized.
RegionPlot
:ImplicitRegionLog[x]y+
x

3
y
1&&
x

x
+xy≥2,{x,y} is not a valid region to plot.
RegionPlot
:RegionPlot called with 1 argument; 3 arguments are expected.
RegionPlot
:ImplicitRegionLog[x]y+
x

3
y
1&&
x

x
+xy≥2,{x,y} cannot be automatically discretized.
General
:Further output of RegionPlot::nnregion will be suppressed during this calculation.
RegionPlot
:ImplicitRegionLog[x]y+
x

3
y
1&&
x

x
+xy≥2,{x,y} is not a valid region to plot.