  Low-resolution LAMOST and Keck spectra of blue supergiant stars distributed
over the disks of the Local Group spiral galaxies M 31 and M 33 are analyzed to
determine stellar effective temperatures, gravities, metallicities, and
reddening. Logarithmic metallicities at the center of the galaxies (in solar
units) of $0.30\pm0.09$ and $0.11\pm0.04$ and metallicity gradients of
$-0.37\pm0.13$ dex/$R_{25}$ and $-0.36\pm0.16$ dex/$R_{25}$ are measured for M
31 and M 33, respectively. For M 33 the 2-dimensional distribution of
metallicity indicates a deviation from azimutal symmetry with an off-centre
peak. The flux-weighted gravity-luminosity relationship of blue supergiant
stars is used to determine a distance modulus of 24.51$\pm$0.13 mag for M 31
and 24.93$\pm$0.07 mag for M 33. For M 31 the flux-weighted gravity--luminosity
relationship (FGLR) distance agrees well with other methods. For M 33 the
FGLR-based distance is larger than the distances from Cepheids studies but it
is in good agreement with work on eclipsing binaries, planetary nebulae ,
long-period variables, and the tip of the red giant branch.
