65 yrs old, missing teeth 18 & 19 with more needing removed: Can I get partial implants?

I am 65 yrs old and missing tooth 18 & 19 which were extracted many years ago. My present dentist wants to extract tooth 17 & 14 because they are infected and cannot be fixed. I also believe #15 & 16 will have to be removed in the near future. I cannot afford to have implants to replace all those teeth. So my question is - can I get implants for #14 & #19 only, and live without the rest of the missing teeth? I still have all my remaining teeth. Your reply will be appreciated. Thanks for your time.