Hypergeometric $\tau$ Function of the $q$-Painlev\'e Systems of Type $(A_2+A_1{)}^{(1)}$

We consider a $q$-Painlev'e III equation and a $q$-Painlev'e II equation arising from a birational representation of the affine Weyl group of type $(A_2+A_1{)}^{(1)}$. We study their hypergeometric solutions on the level of $\tau$ functions.