"equilateral"? Okay.

Okay.Rule 2:

If the solution of two equations is like 0=0, then the equations are equilateral with infinite common solution.

Why is this case different from 0=0? I assume you mean x = 2 or y = 7.Rule 3:

If the solution of two equations is like 2=2 or 7=7 or 9=9, then the equations have only one solution.

Rule #4:

Don't memorize so many rules that you forget to think about what you are doing?