In general, honing your pattern recognition skills to seek out "chunks" of information can be quite useful, as it often saves time and brain space
Here, the (a+b) chunk is common to both, and if you saw that you could combine the equations that way to eliminate variables (the book solution is the multiplication version of the stack & add/subtract method for systems of equation), awesome. If not-- no worries--substitution will still work, and it's a waste of time to pull your hair out if you don't ID a "cool" way to do a problem quickly.
Whenever you have the option, though, some elegant stacking-and-eliminating (or chunking to allow you to eliminate) will cut out a few steps; substitution tends to take longer.
To zoom out to the bigger picture, that ability to ID chunks/patterns in unfamiliar info is what will speed you along on the GMAT, and something that all of the highest scorers do. (Splitting/resplitting on Sentence Correction questions is an example of this. And at the heart of it, that's what all the test prep companies are trying to do-- prepare you to recognize patterns in new material-- GMAT questions on your test day-- by analyzing patterns in old material--retired GMAT questions).
Bigred, you already seem to be aware of this; bravo to you for recognizing that a solution might contain a future-applicable tool rather than being content with a simple explanation. Good luck with your prep!
JP Park | Manhattan GMAT Instructor | Los Angeles
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