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### 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

really stuck.
```

```
Date: 09/09/2001 at 00:00:29
From: Doctor Ian
Subject: Re: How to solve system equations in two variables by

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.

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?

more, or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

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