Starting system:
4x + 6y = 6
6x + 9y = 12
It is often helpful to multiply each equation by a different number to prepare an "ADDITION" which will eliminate one (or in this case both) of the 2 variables:
Multiply the top equation by -3
and the bottom equation by 2:
-12x -18y = -18
 12x  + 18y = 24
Add the terms in each column: 0x + 0y = 6
which is false for all values of "x" and "y".

Since it is not possible to deduce such a false statement from true statements by correct logic, we conclude that the original system cannot be true for any choices of "x" and "y". This system is called

The solution: { } = empty set = Ø