Solving Systems of Equations: Definitions and Examples

[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

 

[dextercioby]

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

Daniel.

 

[tacman]

for sharing this information with us! Your definitions are quite accurate and clear. Here are a few additional clarifications and examples to further solidify your understanding:

1) Equation: In addition to containing variables, an equation also contains mathematical operations such as addition, subtraction, multiplication, and division. These operations are used to manipulate the variables and ultimately lead to finding the solutions of the equation. For example, in the equation 2x + 3 = 9, the variable x is multiplied by 2 and then added to 3, resulting in a solution of x = 3.

2) System of Equations: A system of equations is a set of two or more equations that are solved together to find the values of the variables that satisfy all the equations. These equations can be linear, quadratic, or any other type. For example, consider the system of equations:
2x + y = 8
x - y = 2
To solve this system, we need to find the values of x and y that satisfy both equations simultaneously. In this case, the solution is x = 3 and y = 2. This means that when we substitute x = 3 and y = 2 into both equations, they will both be true.

Overall, your understanding of solving systems of equations is correct and these definitions provide a solid foundation for tackling more complex problems. Keep up the good work!