This is quite a simple question I suppose, but i'm trying to categorise equation types in my mind.
From what I know, linear equations can have any number of variables in them, but in each term there is only one variable e.g. $w+2x-3y+4z=5$
And quadratics have the highest power of any variable in a term having a power of two: e.g. $x^2+2y-3=0$
But when it comes to equations such as $xy+x-2=0$ and $3xy^2-9x+4=0$, are these referred to as quadratics and cubics respectively because of the highest number of variables multiplied together in any one term?
Or perhaps I am thinking about this in the wrong way and there is simply the set of all equations (within which all of the above fall), and there exist subsets of equatios with specific names/categories (e.g. one subset could be 'equations in only one variable' which is formed of the sets 'linear equations', 'quadratics', 'cubics' etc; and another subset could be 'equations in more than one variable but in which each term contains only one variable' in which the subsets are just named y the highest power of any term in the equation i.e. 'linear', 'quadratic' etc...) And so perhaps these other equations just belong to the set of all equations, but not to any other sub-set which has a particular name?
Personally I've never heard anyone refer to an equation like $xy + x - 2 = 0$ as "quadratic." But that's not to say that people don't do it. Just that I've not heard it. However, we do say that it has degree two (or at the very least, the polynomial on the LHS has degree two).
The catch-all term is "nonlinear."