Combine two data sets from two different regions

This is a actually very basic question, but I can't get my head around it. I have two datasets for Europe and U.S. that contain the same two variables. These two variables are in a linear relationsship, which I proved by statistical t-testing. Now I want to check if the two regional differentiated data sets can be combined and are in fact based upon one mechanism. Should I simply combine the data, implement a new linear relationsship and t-test the entirety again on statistical signifance? Or is there a other way? Best!