SOLUTION: what does it mean for a number to be the "solution" to an equation? please give me an example of a variable equation and its solution and please explain in complete sentences how

Question 334642: what does it mean for a number to be the "solution" to an equation?
please give me an example of a variable equation and its solution and please explain in complete sentences how you know that number is the solution.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

A solution of an equation is any entity that can be substituted for the variable or variables such that the the equation is a true statement.

For example, consider the equation

It should be clear that if you replace the

with

, then you have a true statement because 5 plus 3 does indeed equal 8. But if you replace

with any other number, then you have a false statement. Let's see what happens if we use

. 2 plus 3 is 5 which is most assuredly not equal to 8. And the same thing would happen for any other number besides 5 substituted for

.

Point of semantics: You said "...number to be the "solution"..."

Using the word the in that context is only appropriate when you have single variable linear equations. It is more appropriate to say "...a solution" because, in general, there may be more than one. For example,

has two solutions, namely

and

(try it and see for yourself).

Furthermore, some equations have solutions that are not numbers, but ordered pairs of numbers. You see this when you have two-variable equations. For instance,

, has an infinite number of solutions one of which is

.

John

My calculator said it, I believe it, that settles it

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