What is an indeterminate solution?

Question

What is an indeterminate solution?

Answer 1

An indeterminate solution means that there is a solution, but there's no way to pin it down to a single or even a single group of solutions.  For instance, consider the equation

2(x + 4) = 2x + 8

If you solve this for x, you'll end up with something like 0 = 0.  Now, that's certainly true, but it's true regardless of the value of x.  This is an indeterminate solution.  Pick a value for x - any value at all - and it will work just fine.  You can't determine a solution, so "indeterminate".

There are better examples of this than the trivial one I gave you.  They crop up a lot when you study limits at the beginning of calculus.