  We obtain lower bounds on the inverse compressibility of systems whose
Lee-Yang zeros of the grand-canonical partition function lie in the left half
of the complex fugacity plane. This includes in particular systems whose zeros
lie on the negative real axis such as the monomer-dimer system on a lattice. We
also study the virial expansion of the pressure in powers of the density for
such systems. We find no direct connection between the positivity of the virial
coefficients and the negativity of the L-Y zeros, and provide examples of
either one or both properties holding. An explicit calculation of the partition
function of the monomer-dimer system on 2 rows shows that there are at most a
finite number of negative virial coefficients in this case.
