I note, almost every day, that students pay attention only to the operation and don't care about the set on which it works.
I think that it is very important, using examples and counter-examples , to underline the role of the couple (set,operation).

N={0;1;2;...} if n,m in N then (n+m) in N

Z={...;-1;...;+1;...} if u,v in Z then (u+v) in Z

and so on in Q, R, etc.

But using monomials and polynomials:

M={...;a;...;bx;...} and P={...;cx;...;az-cy;..;x+z-y;...}

(a+bx) is in P and not in M.

Note:

In some programming languages data cannot be joined before conversion (warning, error messages).

Find two numbers x,y such that x + y = 11 and x - y = 1. (6;5)

Find two numbers x,y such that x + y = 10 and x - y = 1. (5.5;4.5)

Find two whole numbers x,y such that x + y = 10 and x - y = 1. (!)