Is there a formula that can convert a parametric equation into a Cartesian equation? If there was one, what would be it's implications?

Question

Is there a formula that, upon entering a parametric equation, can output the Cartesian solution to that parametric equation? I ask because some parametric equations are impossible to convert using standard methods, such as (t*e^t,t). 

 

If there was one, what would be it's implications? In other words, what could be done in mathematics, that cannot already be done, with such an equation?

Answer 1

Solve either x or y or z for t.  Plug that into the other equation(s)