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We present an AAOmega spectroscopic study of red giant stars in Bootes I,which is an ultra-faint dwarf galaxy, and Segue 1, suggested to be either anextremely low-luminosity dwarf galaxy or a star cluster. Our focus isquantifying the mean abundance and abundance dispersion in iron and carbon, andsearching for distant radial-velocity members, in these systems.  The primary conclusion of our investigation is that the spread of carbonabundance in both Bootes I and Segue 1 is large. For Bootes I, 4 of our 16velocity members have [C/H] < ~-3.1, while 2 have [C/H] > ~-2.3, suggesting arange of Delta[C/H] ~ 0.8. For Segue 1 there exists a range Delta[C/H] ~ 1.0,including our discovery of a star with [Fe/H] = -3.5 and [C/Fe] = +2.3, whichis a radial velocity member at a distance of 4 half-light radii from the systemcenter. The accompanying ranges in iron abundance are Delta[Fe/H] ~ 1.6 forboth Bootes I and Segue 1. For [Fe/H] < -3.0, the Galaxy's dwarf galaxysatellites exhibit a dependence of [C/Fe] on [Fe/H] which is very similar tothat observed in its halo populations. We find [C/Fe] ~ 0.3 for stars in thedwarf systems that we believe are the counterpart of the Spite et al. (2005)``unmixed'' giants of the Galactic halo and for which they report [C/Fe] ~ 0.2,and which presumably represents the natal relative abundance of carbon formaterial with [Fe/H] = -3.0 to -4.0.  We confirm the correlation between luminosity and both mean metallicity andabundance dispersion in the Galaxy's dwarf satellites, which extends to atleast as faint as Mv = -5. The very low mean metallicity of Segue 1, and thehigh carbon dispersion in Bootes I, consistent with inhomogeneous chemicalevolution in near zero-abundance gas, suggest these ultra-faint systems couldbe surviving examples of the very first bound systems.

Chemical Enrichment in the Faintest Galaxies: the Carbon and Iron Abundance Spreads in the Bo\"otes I Dwarf Spheroidal Galaxy and the Segue 1 System