My dentist showed me my inflected molar on x-ray. if the amoxicillin works, can it be saved?

Depends: The antibiotic may relieve the symptoms of the infected tooth, like pain and swelling, for a period of time, but definitive treatment is indicated. Some teeth are so infected that they cannot be saved. Discuss the prognosis of the tooth with your dentist.

Probably: Your dentist is the best one to get the answer from. If what caused the infection can be treated then the tooth can be saved. You may have a deep cavity causing the infected tooth, in which case you would need a root canal and crown. If it is an infection of the gum and bone (periodontal disease) then it needs to be treated if not to advanced. Again talk to your dentist.

If the infection: Is coming from periodontal tissues and you still have enough bone to support the tooth in conjunction with perio treatment, very likely. If the nerve is also infected, you also need a root canal. Antibiotics will help treat the area where the blood stream can access but not a pathway clogged by a dead tissue.