Implementation process of mixed finite element method

Hello, I am using mixed finite element method to solve a PDE. Theoretically,

the following two equations are obtained, in which there are two unknown quantities u, p,

A * u+B * p=b1;

C * p+D * u=b2;

How does freefem++ implement this solution process?

Is p=C^ (-1) * (b2-D*u) brought into the first equation group? If matrix C is irreversible?