  Recently a certain $q$-Painlev\'e type system has been obtained from a
reduction of the $q$-Garnier system. In this paper it is shown that the
$q$-Painlev\'e type system is associated with another realization of the affine
Weyl group symmetry of type $E_7^{(1)}$ and is different from the well-known
$q$-Painlev\'e system of type $E_7^{(1)}$ from the point of view of evolution
directions. We also study a connection between the $q$-Painlev\'e type system
and the $q$-Painlev\'e system of type $E_7^{(1)}$. Furthermore determinant
formulas of particular solutions for the $q$-Painlev\'e type system are
constructed in terms of the terminating $q$-hypergeometric function.
