How and why is the two-hybrid system used to find where two proteins interact? Use a real example. ...

Two-hybrid screening is used to detect protein-protein or protein-DNA interactions by testing for physical binding. You will look for the activation of a reporter gene when a transcription factor binds to an upstream activating sequence. In a two-hybrid screen, the transcription factor is broken into two fragments: the binding domain (BD), which binds to the UAS, and the activation domain (AD), which activates transcription of the reporter gene. For instance, the yeast two-hybrid screen uses a protein that is translationally fused to a Gal4 BD and another protein to a Gal4 AD.
If the proteins interact, the two Gal4 elements are brought together and transcription occurs.