An eye cannot be myopic and hyperopic at the same time. But an eye can be myopic and presbyopic at the same time.
Hyperopia is not the same as presbyopia. Unfortunately, a lot of people get confused and call presbyopia longsightedness, when it is not.
Presbyopia is the loss of autofocusing power of the eye as the person gets older. Since the eye cannot autofocus, the person needs a certain power for distance, and a different power for near.
Hyperopia, or real longsightedness affects people differently. Mainly, hyperopia requires the eye to put in extra effort to focus (accommodate) for any particular distance. For young people, hyperopia is usually not an issue, they usually do not need to wear glasses and they see everything clearly since they can accommodate a lot. But as they get older, the (auto)focusing power gets less, and they will usually need reading glasses at a younger age, and then when they get even older they will also need progressives or different glasses for distance and near.