3x + 2y = 12

9x + 6y = 18

Solving through canceling

3x+2y=12

9x+6y=18

want to cancel the first eq from the 2nd

multiply 3 to the first eq

9x+6y=36

9x+6y=18

subtract the 2nd from the first equation

0x+0y=18

0=18

this is obviously not true, therefore, there are no solutions to this problem

the only way that you would have no solutions to a system of equation is if the two equations are parallel lines