I went for a dental x ray and the machine looked very old. i am afraid if that machine was faulty and if it might have exposed me to a lot of radiation. is it possible and can such an incident cause cancer to me?

1 small dental x-ray, absolutely not. Less radiation than a few hours in the sun. However computerized (digital) x-ray equipment uses minuscule amount of radiation to produce an even better quality image than older film equipment.

Only multiple exposures and no use of a lead apron could cause a cancer. In your case you were not exposed that much. In the US. all x-ray machines are examined for leakage and safety.