xs={0,3,1};ys={0,1,2};

{a,b,c}=Inverse[Transpose[{{1,1,1},xs,ys}]];

L[i_,x_,y_]:=a[[i]]+b[[i]]*x+c[[i]]*y

xmin=Min[xs];xmax=Max[xs];ymin=Min[ys];ymax=Max[ys];

gbase=RegionPlot[L[1,x,y]>0&&L[2,x,y]>0&&L[3,x,y]>0,{x,xmin,xmax},{y,ymin,ymax}]

gb=Table[Plot3D[L[i,x,y],{x,xmin,xmax},{y,ymin,ymax},RegionFunction->Function[{x,y,z},L[1,x,y]>0&&L[2,x,y]>0&&L[3,x,y]>0]],{i,3}]

gc=Table[ContourPlot[L[i,x,y],{x,xmin,xmax},{y,ymin,ymax},RegionFunction->Function[{x,y,z},L[1,x,y]>0&&L[2,x,y]>0&&L[3,x,y]>0]],{i,3}]