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Thanks!

Do Equations in More Than Three Variables Represent Graphs in Higher Dimensions?

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Hey, first of all, I'd like to apologize if I'm posting this in the wrong forum. I wasn't sure whether I should post it here or in the mathematics forum. Recently I was going through an Algebra book, and I saw a chapter on solving linear equations in three variables. The book explained how these sets of equations can be solved using elimination, matrices, Cramer's rule, etc. Anyway, I worked several of these problems. When I was finished, just out of curiosity, I wondered what it would be like if I set up five sets of equations with five variables, and solved them. I created one, and using my preferred technique, elimination, I went about solving it and it went MUCH more smoothly than I expected it would. When I was finished, I had the values that I had started out with, and it had all worked out fine. I used five variables X, Y, Z, K, and J. When I had finished, I went back to the book I was using and saw that linear sentences in two variables represented graphs in two dimensions, and linear equations in three variables represent graphs in three dimensions. So here's my question: Do sets of equations with more than three variables represent graphs in higher dimensions?

P.S: Here are the equations I worked. Feel free to point out anything that I may have done wrong.

2x+4y-1z-6k+2j=-1

3x+6y-3z-8k+4j=1

1x+3y+4z-2k+4j=47

4x-2y-2z+6k+2j=28

5x+3y+4z+3k+3j=69

(The values are X=2, Y=3, Z=5, K=4, J=6).