What happens when the specific immune system encounters this pathogen?

B cells carrying receptors for both Antigen $1$ and Antigen $2$ produce antibodies that recognize the two antigens.

B cells carrying receptors for Antigen $1$ produce antibodies that recognize Antigen $1,$ while different B cells carrying receptors for Antigen $2$ produce antibodies that recognize Antigen $2.$

B cells carrying receptors to the pathogen generate antibodies that recognize the pathogen.