System of equations

1. Feb 8, 2005

C0nfused

Hi everybody,
Here are some definitions that I want you to comment/correct:

1)Equation: An equality that contains variables. The values of the variables(or if we talk about real numbers, the numbers) that make the equality "true" are called solutions of the equation. So when we say "solve the equation of x,y f(x,y)=0" it's the same as " find all the pairs (x,y) so that f(x,y)=0

2)System of equations: a number of equations with the same variables. The values of the variables that make all the equations true simultaneously, at the same time, are called solutions of the system. So when we say "solve the system |f(x,y)=0 " it's the same as " find all the pairs (x,y) so that
|g(x,y)=0
f(x,y)=0 and g(x,y)=0 at the same time with (x,y)=the pairs we have found"
, or "find which solutions of f(x,y)=0 are also solutions of g(x,y)=0"
(these refer to any system of any number of equations)

Are these correct?(just checking if i have correct understanding of this really important subject)

Thanks

2. Feb 8, 2005

dextercioby

Yes,they are correct.At the first,it's more general to include equations in C as well.

Daniel.