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 Post subject: GMAT Algebra
PostPosted: Wed May 26, 2010 3:29 pm 
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Joined: Tue Apr 13, 2010 8:48 am
Posts: 478
If we add the equations, the b terms cancel out, yielding:
(3ab = 1)
+
(4a + b = 6)

7a = 7
a = 1

My question is how do you know when you should be adding equations together (The step referenced above). I know there has to be a fundamental concept I am forgetting. I think I tried the solving for a and then substituting the answer into the other equation, therefore treating each equation as if they are mutually exclusive. Please explain the correct approach/rationale and how to make the correct determination. Thanks.


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 Post subject: Re: math: algebra, solving a system of equations
PostPosted: Wed May 26, 2010 3:35 pm 
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The most obvious reason to add equations together or subtract one from another is having one of the variables with the same constant multiplier (or opposite, e.g. 3 and -3).
a + 3b = 7
2a – 3b = 7
or
a + 3b = 7
2a + 3b = 7

If we consider this specific question then you can see that we could subtract one from another right from the beginning :
a – (b/3) = 1/3

a + (b/4) = 3/2

a – (b/3) – a – (b/4) = 1/3 – 3/2
– (b/3) – (b/4) = 1/3 – 3/2
We got rid of variable a, though we have to deal with factors.
-(7b/12) = -(1/6)
b = 2


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