  In this article we prove solvability results for $L^2$ boundary value
problems of some elliptic systems $Lu=0$ on the upper half-space $\R^{n+1}_{+},
n\ge 1$, with transversally independent coefficients. We use the first order
formalism introduced by Auscher-Axelsson-McIntosh and further developed with a
better understanding of the classes of solutions in the subsequent work of
Auscher-Axelsson. The interesting fact is that we prove only half of the
Rellich boundary inequality without knowing the other half.
