If we add the equations, the b terms cancel out, yielding: (3a – b = 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.
Post subject: Re: math: algebra, solving a system of equations
Posted: Wed May 26, 2010 3:35 pm
Joined: Fri Apr 09, 2010 2:11 pm Posts: 453
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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