a={{2,-1,1},{1,1,2.}};b={13,1};
{u,w,v}=SingularValueDecomposition[a];
u.w.Transpose[v]
f[x_]:=If[x==0,0,1/x];SetAttributes[f,Listable];
w1=f[Transpose[w]]
xx=v.w1.Transpose[u].b
Clear[x,y,z];r=Thread[a.{x,y,z}==b]
d=7;Show[ContourPlot3D[Evaluate[r],{x,-d,d},{y,-d,d},{z,-d,d}],Graphics3D[{Red,PointSize[0.05],Sphere[xx]}]]