Solving Equations in Two Variables by Addition/Subtraction
Date: 09/08/2001 at 16:43:06 From: nasha Subject: How to solve system equations in two variables by addition and subtraction The problem is 2x + 3y = 7 4x - 5y = 25 I have no idea how to solve this problem at all. Please help me; I'm really stuck.
Date: 09/09/2001 at 00:00:29 From: Doctor Ian Subject: Re: How to solve system equations in two variables by addition and subtraction Hi Nasha, Suppose for a moment that we are trying to solve a slightly different problem: 2x + 3y = 7 2x + 4y = 10 Just looking at the two equations, we can see that an extra y on the left side corresponds to an extra 3 on the right side. So we know that y = 3 without having to do anything. If instead we have 2x + 3y = 7 2x - 4y = 21 In this case, see that a loss of 7y on the left (from + 3y to - 4y) corresponds to a gain of 14 on the right. So we know that -7y = 14, or y = -2. By now, you might be wishing that you had to solve a problem like this, instead of the one that you were given. But wait! Is there a way that you can turn your problem into a problem like this? What if you multiply everything in the first equation by 2? Then you would have 4x + 6y = 14 4x - 5y = 25 Can you take it from here? I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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