You perform an experiment and proceed to recrystallize the product in an ethanol:water solvent mixture. why is a mixed solvent system used instead of just one component or the other?

It seems that you have missed the necessary options for us to answer this question. But anyway, hope this answers it. Upon performing an experiment and proceeded to recrystallizing the product in an ethanol:water solvent mixture, the mixed solvent system is used instead of just one component or the other because we want to control the solubility of the product.

First if you use a mixed solvent of ethanol water system, it is much cheaper if it is pure ethanol. by using the the proper ratio of the both solvent you can crystallize the product effectively. unlike if pure ethanol, it is very volatile then the product might not recrystallize properly.