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### 4-Variable Systems of Equations

```Date: 12/10/2002 at 21:50:21
From: Aaron Igdalsky
Subject: Solving 4 Variable Systems of Equations

I am stumped!

2w-x+5y+z=-3
3w+2x+2y-6z=-32
w+3x+3y-z=-47
5w-2x-3y+3z=49
```

```
Date: 12/11/2002 at 10:50:15
From: Doctor Ian
Subject: Re: Solving 4 Variable Systems of Equations

Hi Aaron,

Do you remember how to solve a system with two equations and two
variables by substitution? This works the same way, but has more
steps.

Suppose we take the first equation, and solve it for z:

z = -2w + x - 5y - 3

Now we can replace z in the other equations to get

3w + 2x + 2y - 6(-2w + x - 5y - 3) = -32

w + 3x + 3y -  (-2w + x - 5y - 3) = -47

5w - 2x - 3y + 3(-2w + x - 5y - 3) =  49

Simplify these, and you'll end up with three equations and three
variables. Try the same trick again with another variable, and you'll
have two equations in two variables.

Is this enough to get started?

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

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