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