SOLUTION: x+2y=4 2x-y=1 If I am asked to solve by Gaussian Elimination, is that the same as solving by the addition method, also known as the elimination method? Confusing terms??

Question 246858: x+2y=4
2x-y=1
If I am asked to solve by Gaussian Elimination, is that the same as solving by the addition method, also known as the elimination method? Confusing terms??
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The difference is quite subtle, and certainly a source of confusion, at least until you have a semester of Linear Algebra under your belt.

If you simply use the elimination algorithm on the equations themselves, then The Addition Method, The Elimination Method, and Gaussian Elimination are utterly equivalent terms. At this stage, I like to call it Elimination because it most accurately describes what you are trying to accomplish.

The difference arises when you start to solve more complex systems using augmented matrices. With matrices, you don't actually have an Addition Method or an Elimination method, per se. You use Gaussian Elimination or its extension, Gauss-Jordan Elimination. I certainly wouldn't bother messing about with an augmented matrix to solve this rather simple do-it-in-your-head 2-by-2. So, for your purposes, call it all the same thing.

John

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