(*Nasser M. Abbasi, 3/15/16*)

eq1=2 x1+3 x2==1;
eq2=x1+x2+x3==1;
len=2;
g2=Graphics3D[Simplex[{{1,0,0},{0,1,0},{0,0,1}}]];
g1=ContourPlot3D[Evaluate@eq1,{x1,-1,1},{x2,-1,1},{x3,-1,1},ContourStyle->Directive[FaceForm[Yellow],Opacity[.5]], Mesh->None,Lighting->{{"Ambient",White}},Boxed->True,Axes->False];
g3=Graphics3D[{
Arrow[{{0,0,-len},{0,0,len}}],Text[Style[z,Bold],{0,0,1.1len}],
Arrow[{{0,-len,0},{0,len,0}}],Text[Style[y,Bold],{0,1.1 len,0}],
Arrow[{{-len,0,0},{len,0,0}}],Text[Style[x,Bold],{1.1len,0,0}],
{Blue,Sphere[{0,1/3,2/3},.05]},
{Blue,Sphere[{1/2,0,1/2},.05]},
{Red,Thick, Line[{{0,1/3,2/3},{1/2,0,1/2}}]}
}];
Grid[{{Column[{eq1,eq2}]},
{Show[g1,g2,g3,PlotRange->All,ImageSize->400,SphericalRegion->True]}}]