  We investigate the X-ray properties of three interacting luminous infrared
galaxy systems. In one of these systems, IRAS 18329+5950, we resolve two
separate sources. A second, IRAS 20550+1656, and third, IRAS 19354+4559, have
only a single X-ray source detected. We compare the observed emission to PSF
profiles and determine that three are extended in emission. One is compact,
which is suggestive of an AGN, although all of our profiles have large
uncertainties. We then model the spectra to determine soft (0.5--2 keV) and
hard (2--10 keV) luminosities for the resolved sources and then compare these
to relationships found in the literature between infrared and X-ray
luminosities for starburst galaxies. We obtain luminosities of
$\log(L_{\textrm{soft}}/\textrm{L}_{\odot}) = 7.32,\:7.06,\:7.68$ and
$\log(L_{\textrm{hard}}/\textrm{L}_{\odot}) = 7.33,\: 7.07,\: 7.88$ for IRAS
18329+5950, IRAS 19354+4559, and IRAS 20550+1656, respectively. These are
intermediate to two separate predictions in the literature for
star-formation-dominated sources. Our highest quality spectrum of IRAS
20550+1656 suggests super-solar abundance of alpha elements at $2\sigma$
significance, with $\log(\frac{\alpha}{\alpha_{\odot}}) = [\alpha] =
0.4\pm0.2$. This is suggestive of recent enrichment with Type II supernovae,
consistent with a starburst environment. The X-ray properties of the target
galaxies are most likely due to starbursts, but we cannot conclusively rule out
AGN.
