  A large number of $B_c$ meson events have been recorded at the LHCb detector,
especially some two-body hadronic decay modes. We analyzed the weak decays of
the $B_c$ meson into two hadron states under the flavor SU(3) symmetry. The
relations among amplitudes of $B_c$ into $ D+P(V)$, $B+P(V)$, $P(V)+P(V)$,
$T_8+\bar T_8$ and $T_{10}+\bar T_{10}$ were investigated systematically, where
$P$ ( $V$) denotes a light pseudoscalar (vector) meson and $T_{8,10}$ denotes a
light baryon. The $\eta-\eta'$ mixing and $\omega-\phi$ mixing effects are also
considered for the phenomenological discussions. We obtained the relations
among decay widths of different $B_c$ decay channels. These results are helpful
to study the two-body decay properties of the $B_c$ meson and test the flavor
SU(3) symmetry.
