  The chiral and superconducting gaps are studied in the context of a planar
fermion model with four-fermion interactions. The effect of the tilt of the
Dirac cone on both gaps is shown and discussed. Our results point to two
different behaviors exhibited by planar fermionic systems. We show that there
is a threshold value $\tilde{t}^*$ for the effective tilt parameter such that
when $|{\bf \tilde{t}}| < \tilde{t}^*$, the superconducting phase persists for
negative values of the superconducting coupling constant. For positive values
of the superconducting coupling constant, the induction of a superconducting
gap by a chemical potential exists and which is similar to the one seen in
graphene-like systems. For $|{\bf \tilde{t}}| > \tilde{t}^*$ and a negative
superconducting coupling constant, the superconducting phase can be present,
but it is restricted to a smaller area in the phase portrait. Our analysis also
shows that when $|{\bf \tilde{t}}| > \tilde{t}^*$ and for positive values for
the superconducting coupling constant, the induction of a superconducting gap
in the presence of a chemical potential is ruled out. In this case, the
increase of the chemical potential works in favor of the manifestation of a
metallic phase.
