To plug-in or not to plug-in

Yesterday i was just skimming through the algebra section in PR. There was a concept called plug-in which is nothing but trial-and-error method in our language. Various types of problems were discussed for which the method to plug-in was discussed.
I was not convinced to use this method for two reasons.
1. Solving thru' algebra equations gives me confidence.
2. I do it quickly with equations itself than substituting and finding out.
Anyway it is a good technique especially for questions involving fractions and set theory.
Ex - 1/2 were boys 1/3 were both boy and girl how many girls were there.
If we assume there are 6 as total ppl, it is easy to solve. 6 is selected because it is the LCM of the denominator of the fractions