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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 and third source, IRAS 19354+4559 and IRAS 20550+1656, have only a single X-ray source detected. We compare the observed emission to point-spread function (PSF) profiles and determine that they are all consistent with the PSF, albeit with large uncertainties for some of our sources. We then model the spectra to determine soft (0.5-2 keV) and hard (2-10 keV) luminosities for the resolved sources and compare these to relationships found in the literature between infrared and X-ray luminosities for starburst galaxies. We obtain luminosities (0.5-10 keV) ranging from 1.7 to 7.3 × 1041 erg s–1 for our systems. These X-ray luminosities are consistent with predictions for star-formation-dominated sources and thus are most likely due to starbursts, but we cannot conclusively rule out active galactic nuclei. [ABSTRACT FROM AUTHOR]