a={{4,3},{3,4},{2,-2}}; b={1,7,-2};
{u,w,v}=SingularValueDecomposition[a]
u.w.Transpose[v]
Clear[x,y];r=Thread[a.{x,y}==b];
f[x_]:=If[x==0,0,1/x];SetAttributes[f,Listable];
w1=f[Transpose[w]]
xx=v.w1.Transpose[u].b
d=5;ContourPlot[Evaluate[r],{x,-d,d},{y,-d,d},Epilog->{Red,PointSize->Large,Point[xx]}]