Thanks for your reply!

My book calls the system xy=3 x+y=4 quadratic...

I guess because if you substitute y=4-x into xy=3 you get a quadratic equation for x.

As I see, in terms of single equations the form of the equation does not matter. If an equation is quadratic then all other equations equivalent with it will also be quadratic.

So maybe extending this to simultaneous equations we can define a quadratic equation system as one that can be rearranged in equvalent steps into a form where the highest degree/order* of the part-equations is 2.

But this is just what I put together by looking at examples...

* I mean the thing that is 2 for quadratic, 3 for cubic, I dont know the word.