  We perform combined resistivity and compressibility studies of
two-dimensional hole and electron systems which show the apparent
metal-insulator transition - a crossover in the sign of dR/dT with changing
density. No thermodynamic anomalies have been detected in the crossover region.
Instead, despite a ten-fold difference in r_s, the compressibility of both
electrons and holes is well described by the theory of nonlinear screening of
the random potential. We show that the resistivity exhibits a scaling behavior
near the percolation threshold found from analysis of the compressibility.
Notably, the percolation transition occurs at a much lower density than the
crossover.
