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When to subtract?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by cmr209 » Wed Sep 09, 2009 2:44 pm
With the following problem:
m + 2n = 13 and 3m + 2n = 21

How do I know to add or subtract the two equations?
The word "and" generally tells me to add, yet in this case it appears that they need to be subtracted.
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by bharathh » Wed Sep 09, 2009 3:02 pm
Depends on which term you are solving for. You want to subtract to get rid of a particular term.

In this case it is easy to get rid of all the n terms by subtracting the equations. Solve for m and then plug in the value of m to find n.
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by grockit_jake » Sun Sep 13, 2009 9:00 am
Adding and subtracting equations is important and good to keep in mind, but there is no rule.

It depends what variables the question is asking for, and in what capacity.

In your given set:


m + 2n = 13
3m + 2n = 21

You can see that since the n's have the same coefficient, you can subtract and be left with m's only. If you add, you will see nothing will drop out.

Also, be careful not to screw up your signs if you subtract in the wrong direction ( -2m = -8 OR 2m = 8)
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