  Granular systems are not always homogeneous and can be composed of grains
with very different mechanical properties. To improve our understanding of the
behavior of real granular systems, in this experimental study, we compress 2D
bidisperse systems made of both soft and rigid grains. By means of a recently
developed experimental set-up, \md{from the measurement of the displacement
field we can} follow all the mechanical observables of this granular medium
from the inside of each particle up-to-the whole system scale. We \md{are able
to} detect the jamming transition from these observables and study their
evolution deep in the jammed state for packing fractions as high as $0.915$. We
show the uniqueness of the behavior of such a system, \md{in which way} it is
similar to purely soft or rigid systems and how it is different from them. This
study constitutes the first step toward a better understanding of the
mechanical behavior of granular materials that are polydisperse in terms of
grain rheology.
