simultaneous equations vs system of equations

[hanky]

I would like to know whether "simultaneous equations" and "system of equations" are the same?
If not, please show me the difference. Thank you.

[BobK]

Simultaneous equations:

A + B = C
E + F = C
Find E in terms of F, A, and B.

I 've never heard of 'system of equations' as a collocation, although it would be easy enough to think up an appropriate context (with some system made up of equations). But maybe in some form of English this is a collocation, so it'd be misleading for me to do that.

b

[hanky]

Simultaneous equations:



I 've never heard of 'system of equations' as a collocation, although it would be easy enough to think up an appropriate context (with some system made up of equations). But maybe in some form of English this is a collocation, so it'd be misleading for me to do that.

b

If you google two phrases you will figure out that "Simultaneous equations" is less popular than "system of equations". Anyway, do you think that they are the same?

[BobK]

If you google two phrases you will figure out that "Simultaneous equations" is less popular than "system of equations". Anyway, do you think that they are the same?

"Simultaneous equations" have - and the phrase has - a specific use; those two words will rarely if ever occur together in contexts that aren't like the one I gave as an example (although it was a trivial example, and in real life the equations involved will almost always be a lot more complex). The odds against "system" and "equations" occurring, linked by "of", in a range of contexts, must be much lower. So the Google results don't surprise me at all.

I have no reason to think they mean the same; I don't see why you feel the Google results suggest that they do. They don't, in Br English, although every set of simultaneous equations can be seen as a system. In my example there were only two, but in this system there are many more:

A=B
B=C
C=D
D=E
...etc

So I suppose that in some dialect of English a large enough set of simultaneous equations may be called a "system of equations"; but it's not a usage I've met.

b

[Jaskin]

Hello,
Not a teacher but I like maths

Linear algebra (modular mathematics series) by Reg Allenby

"Solutions of systems of simultaneous linear equations (also called linear systems) arise in very many real life situations; for just a couple of instances see..."

I've checked google results for Uk only and for USA only;
It's seems to be a difference between AmEn and BrEn where "Simultaneous linear equations" is more often used in BrEn and "system of linear equations" is more often in AmEn

Cheers

[SUDHKAMP]

I would like to know whether "simultaneous equations" and "system of equations" are the same?
If not, please show me the difference. Thank you.

Yes, both the terms mean the same. In Algebra books which were written in the beginning of 20th century, you would find the terms simultaneous equations. They refer to the linear equations, in which you had to find the value of x,y,z where the values of different combinations were given. A student was required to find the value of these unkonwn variables by using methods like substitution, elimination or Matrices.
Since these set of equations had the same value for variables and they formed the same set of values, they were also called the 'system of equations'.
These system of equations could be linear equations or non-linear equations.
Hence, it is more the change in usage of language in view of set theory that simultaneous equations are being called a system of equations while asking a problem to the student.

P.S. : I am not a teacher of English language, but just someone who loves the language.(and studied Mathematics as a major subject in graduation).

[BobK]

...

I have no reason to think they mean the same...

... I suppose that in some dialect of English a large enough set of simultaneous equations may be called a "system of equations"; but it's not a usage I've met.

b

Hello,
Not a teacher but I like maths

Linear algebra (modular mathematics series) by Reg Allenby
I've checked google results for Uk only and for USA only;
It's seems to be a difference between AmEn and BrEn where "Simultaneous linear equations" is more often used in BrEn and "system of linear equations" is more often in AmEn

Cheers

You live and learn

b