# Question #ac581

##### 2 Answers

#### Answer:

No, not every equation has **an answer.**.

There is a whole range of possibilities.

#### Explanation:

No, not every equation has **an answer.**

A linear equation usually has **one answer** ,

while a quadratic **two answers**

and a cubic equation (**three answers** and so on.

There are some equations (which are actually identities) which solve to give the result:

This is a true statement, but there is no variable left to solve for.

This means that t **he variable can have any value.** ..

Thus there are **infinitely many solutions/answers.**

On the other hand, sometimes equations solve to give:

This is a false statement without a variable. It means that equation cannot be solved, **there is no solution, and the variable has no value.**

In solving an equation you might end up with

Division by 0 is not allowed, so this solution would be **undefined.**

Some equations end up with the result.

These equations do not have any real number as a solution and you end up working in the **world of the complex numbers** .

#### Answer:

Not every equation has a solution. Every equation has a solution set. But the solution set for some equations is empty. (There are no solutions.)

#### Explanation:

Sometimes we give solutions of equations using a list, other times we use the solution set. (Don't be intimidated by 'set'. A set is a container -- like a box-- that may or may not have things in it.)

**Examples**

For

For

For

For

There is still a set (box) of solutions, there just isn't anything in the box (set). The solution set is

For