No, not every equation has an answer..
There is a whole range of possibilities.
No, not every equation has an answer.
A linear equation usually has one answer ,
while a quadratic
and a cubic equation (
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 .
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.)
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.)
There is still a set (box) of solutions, there just isn't anything in the box (set). The solution set is