What is a System of Equations? And its Solution?

Here is an example of a system of equations (also called a simultaneous system of equations)
x² + y = 3 (1)
15x + 3y = 21
It's simply a bunch of equations we want to find a single solution for. Though it usually isn't said out loud, the word "and" is always implied:
x² + y = 3 and 15x + 3y = 21.

This means both equations are supposed to be true.

Each equation, by itself, has many solutions. For example, if x = 0 and y = 3 then the first equation is true. But the second equation isn't.
On the other hand, if x = 1 and y = 2 , then both equations are true. So we'll say this is a solution of the system.