The mixture of language families is mainly a consequence of migration. In the case of Hungarian, there is historical evidence that the Magyars brought their language from the steppes of Asia with them when they settled in Europe. In the case of Basque, there is no historical evidence, but it might be just the other way round: Basque might have been there before the Indo-Europeans migrated from their homeland, possibly south eastern Europe, in this part of Europe.
Attempts have been made to infer where the Indo-Europeans originally came from on account of their language. This is highly complicated because there is little historical evidence and we have to try to draw conclusions from language. Can you imagine how this might work? What does the vocabulary of a people tell us about their life, which conclusions can we make about where they lived on the basis of the words they had or did not have?
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