  We present chemical abundances of red giant branch (RGB) stars in the dwarf
spheroidal (dSph) satellite system of Andromeda (M31), using spectral synthesis
of medium resolution (R $\sim 6000$) spectra obtained with the Keck II
telescope and DEIMOS spectrograph via the Spectroscopic and Photometric
Landscape of Andromeda's Stellar Halo (SPLASH) survey. We coadd stars according
to their similarity in photometric metallicity or effective temperature to
obtain a signal-to-noise ratio (S/N) high enough to measure average [Fe/H] and
[$\alpha$/Fe] abundances. We validate our method using high S/N spectra of RGB
stars in Milky Way globular clusters as well as deep observations for a subset
of the M31 dSphs in our sample. For this set of validation coadds, we compare
the weighted average abundance of the individual stars with the abundance
determined from the coadd. We present individual and coadded measurements of
[Fe/H] and [$\alpha$/Fe] for stars in ten M31 dSphs, including the first
[$\alpha$/Fe] measurements for And IX, XIV, XV, and XVIII. These fainter, less
massive dSphs show declining [$\alpha$/Fe] relative to [Fe/H], implying an
extended star formation history. In addition, these dSphs also follow the same
mass-metallicity relation found in other Local Group satellites. The
conclusions we infer from coadded spectra agree with those from previous
measurements in brighter M31 dSphs with individual abundance measurements, as
well as conclusions from photometric studies. These abundances greatly increase
the number of spectroscopic measurements of the chemical composition of M31's
less massive dwarf satellites, which are crucial to understanding their star
formation history and interaction with the M31 system.
