simultaneous equations

The word simultaneous means happening at the same time, and that captures the idea perfectly: these are equations you must satisfy together, in the same instant, with one consistent choice of the unknowns. You are not allowed to pick numbers that work for one equation but break another.

Simultaneous equations is, in everyday usage, just another name for a system of equations — the term is especially common in British and Commonwealth textbooks. Solving them means finding the value or values of the variables that make all the equations true at once.

The emphasis on at the same time is the heart of the matter. If you solved each equation in isolation you would usually get a whole line of possibilities for each; the simultaneous requirement is what cuts those possibilities down to where they overlap. That overlap may be a single point, nothing, or an entire shared line.