  We present a method for solving the lightcurve of an eclipsing binary system
which contains a Cepheid variable as one of its components as well as the
solutions for three eclipsing Cepheids in the Large Magellanic Cloud (LMC). A
geometric model is constructed in which the component stars are assumed to be
spherical and on circular orbits. The emergent system flux is computed as a
function of time, with the intrinsic variations in temperature and radius of
the Cepheid treated self-consistently. Fitting the adopted model to photometric
observations, incorporating data from multiple bandpasses, yields a single
parameter set best describing the system. This method is applied to three
eclipsing Cepheid systems from the MACHO Project LMC database: MACHO ID's
6.6454.5, 78.6338.24 and 81.8997.87. A best-fit value is obtained for each
system's orbital period and inclination and for the relative radius, color and
limb-darkening coefficients of each star. Pulsation periods and
parameterizations of the intrinsic color variations of the Cepheids are also
obtained and the amplitude of the radial pulsation of each Cepheid is measured
directly. The system 6.6454.5 is found to contain a 4.97-day Cepheid, which
cannot be definitely classified as Type I or Type II, with an unexpectedly
brighter companion. The system 78.6338.24 consists of a 17.7-day, W Vir Class
Type II Cepheid with a smaller, dimmer companion. The system 81.8997.87
contains an intermediate-mass, 2.03-day overtone Cepheid with a dimmer, red
giant secondary.
