  We consider two Ito equations that evolve on different time scales. The
equations are fully coupled in the sense that all coefficients may depend on
both the "slow" and the "fast" processes and the diffusion terms may be
correlated. The diffusion term in the "slow" process is small. A large
deviation principle is obtained for the joint distribution of the slow process
and of the empirical measure of the fast process. By projecting on the slow and
fast variables, we arrive at new results on large deviations in the averaging
framework and on large deviations of the empirical measures of ergodic
diffusions, respectively. The proof of the main result relies on the property
that exponential tightness implies large deviation relative compactness. The
identification of the large deviation rate function is accomplished by
analysing the large deviation limit of an exponential martingale.
