Question

Is there such thing as a equation that only uses variables and functions but has only one answer?

Answer 1

Mathematically, it's either on of these three for one equation:

0. It has exactly ,one ,solution

,

1. It has multiple solutions

,

2. It has no solution

Now, since the equation you're describing uses only variables (assuming you use more than one and no independent numeric values), you're ruling out option 1. We're left with:

• It has multiple solutions

,

• It has no solution

Let's take a look at the equation

`y=x`

And its graph:

The line that the equation sketches is constructed by all the points (x, y) that are a valid solution for the equation.

In fact, when you have an equation with only variables, you'll get inifite solutions!

So there's no such thing as an equation with only variables that has a unique solution. They all sketch some kind of curve, or line, in the plane with the infite set of points that satisfy the expression.