# Solving System of Equations w/ Gauss-Jordan Elimination

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## Main Question or Discussion Point

I am fairly new here so I apologize for any mistakes in my post.

My question concerning solving a system of equations using Gauss-Jordan Elimination is specifically about different ways to handle a possible constant. Say for instance you have three equations:

1. X1+X2+X3 + 3 = 9
2. 2X1+4X2+X3 = 13
3. X1+2X2+2X3 = 11

Note: I am sorry if this post is jumbled, I am just trying to hop into this community and I decided to post on something that I have been thinking on even though it seems kind of trivial. Thanks to everyone in advance for any sort of discussion, I hope to become active in this community as I find many of these topics very interesting.

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BvU
Homework Helper
2019 Award
could you perhaps take out the constant of 1
what constant would that be, specifically ?
take all the constants present, divide it by the number of variables
could you work out in detail what you mean ? 'it' ? or 'them' ? or 'all of them' ?

Mark44
Mentor
This doesn't make much sense.
"Subtract 3 from the answer..." -- the "answer" will be a triple of numbers.
"Take all the constants present, divide it by the number of variables..." Who is "it" here? Does "it" refer to the sum of all the constants? In any case, adding the constant terms and then dividing this sum by the number of equations will give you a number that is unrelated to anything.

There is a standard technique, Gauss-Jordan elimination, for solving systems of equations. You must have at least heard of this, as you have it in your thread title. This technique entails writing the equations in what is called an augmented matrix, and then reducing the matrix to give solutions for the variables.

The underlying geometry for the system you showed is three planes in three-dimensional space. If there is a unique solution, this means that all three planes intersect at only a single point. Other possibilities are that the planes don't intersect at all (possibly all of the planes are parallel to each other) or that the planes intersect in a line, in which case there are an infinite number of solutions; namely, all of the points on the line of intersection.

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