How did Europeans in rural areas respond to the increasing population and pressures on traditional family life that accompanied the Industrial Revolution?

They emigrated, often to the United States.

Explanation:

When the Industrial Revolution took place, the number of people in Europe significantly increased. Previously, most Europeans had been living in little farms, and by the 20th Century, most of them moved to cities.

This represented a drastic change in traditional family life since working-class people lived in substandard housing, under poor conditions and exposed to diseases. Also, the family became more separate, since men had to work for long hours and women stayed at home to look after their children. For this reason, many of them emigrated to America in the hope of finding better economic opportunities.