Set of linear equations and simultaneous linear equations

Click For Summary

Discussion Overview

The discussion revolves around the relationship between a set of linear equations and simultaneous linear equations, exploring whether they are equivalent or if there are nuances that differentiate them. The scope includes conceptual clarification and technical explanation.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • Nobahar questions whether a set of x linear equations is the same as x simultaneous linear equations and seeks to understand any potential nuances.
  • Some participants suggest that the distinction may arise if the equations involve different variables.
  • A later reply indicates that the classification of equations as simultaneous depends on the rule for the set, asserting that a collection of equations relevant to a system would be considered simultaneous.
  • There is an assumption that the number of variables must be relevant to the equations in the set for them to be classified as simultaneous.

Areas of Agreement / Disagreement

Participants express varying views on the equivalence of the two concepts, with some suggesting conditions under which they may differ. The discussion remains unresolved regarding the nuances and definitions involved.

Contextual Notes

Limitations include potential ambiguity in definitions of "set" and "simultaneous," as well as the relevance of variables in determining the classification of equations.

nobahar
Messages
482
Reaction score
2
Hello!
Quick and silly question; my apologies, but it shouldn't take to long to answer!
Is a set of x linear equations the same as x simultaneous linear equations?
I'm pretty sure they are, but are there any nuances I'm overlooking? Is there any thing that can be considered one but not the other?
Many thanks,
Nobahar.
 
Physics news on Phys.org
Only thing I could think of is if they had different variables.
 
Ah! Thanks JonF.
 
Is a set of x linear equations the same as x simultaneous linear equations?

This depends on the rule for the set. The set of equations which belongs to a system would be a collection of simultaneous equations. If this is the case under consideration, then the answer is Yes. This assumes that the x number of variables are relevant to this set of equations to describe the system.

The best that I can understand what you are asking is that, Yes! More advanced forum members can more fully examine the finer details.
 
Thanks symbolipoint.
 

Similar threads

High School Attempt to solve this system of three linear equations
  • · Replies 10 ·
Replies
10
Views
3K
High School What Does 'Simultaneous' Mean in Linear Equations?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Basis for set of solutions for linear equation
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Canonical Form for quadratic equations *with* linear terms
  • · Replies 4 ·
Replies
4
Views
3K
High School System of linear equations: When are we guaranteed a unique solution?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad The Price of Beer - Linear Algebra Problem
  • · Replies 44 ·
2
Replies
44
Views
5K
Undergrad Is the set {e^x, x^2} linearly independent?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Interpretation: Solution to a set of Linear Equations
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Showing a set is a basis for a vector space
  • · Replies 2 ·
Replies
2
Views
2K
High School How can I properly distribute fractions when solving a set of linear equations?
  • · Replies 7 ·
Replies
7
Views
2K