Starting system:

4x + 6y = 8
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 = +24
12x - 18y = 24

Add the terms in each column : 0x + 0y = 0 (an identity)

This means that the two equations make identical statements about "x" and "y". Hence the two equations have identical graphs; any point on this graph solves both equations in the system. This system has many solutions, and is called
DEPENDENT.

The solution in set notation : { (x,y) | 4x + 6y = 8 }