a={{4,3,2},{3,4,-2}};b={-10,9};
{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]}]]