All words starting with the prefix Eco- are Greek. Eco- comes from Ancient Greek οἶκος, oikos, which means house, household. A few examples are:
Economy. From Ancient Greek οἰκονομία, oikonomia, management of a household, administration. From οἶκος, oikos + νόμος, nomos, law. Effective management of the resources of a community or system.
Derived or related words: economic, economical, economist, economize, economically etc.
Ecology. From Ancient Greek οἰκολογία. From οἶκος, oikos + -λογία, -logia, study of something. The branch of biology dealing with the relationships of organisms with their environment and with each other.
Derived or related words: ecologic, ecological, ecologist, ecologically.
Ecotourism. From οἶκος, oikos + tourism. Responsible travel to natural areas supporting the fauna, flora, and local economy.
Ecosystem. From οἶκος, oikos + σύστημα, sustēma,, organised whole, body. From σύν, syn, with, together + ἵστημι, histēmi, I stand. A system formed by an ecological community and its environment that functions as a unit.
Derived or related words: ecosystemic.