In this short note, we give a construction of solutions to the Einstein constraint equations using the well known conformal method. Our method gives a result similar to the one of Holst-Nagy-Tsogtgerel and Maxwell, namely existence when the so called TT-tensor is small and the Yamabe invariant of the manifold is positive. The method we describe is however much simpler than the original method and allows easy extensions to several other problems. Some non-existence results are also considered.