Answer
There is no real solution to the system of equations.
It is inconsistent.
Graphing both equations, the functions don't intersect.
Work Step by Step
1) $2x-3y=2$
2) $6x-9y=3$
If we multiply the first equation by 3, we get:
2) $3\times(2x-3y)=3\times(2)$
2) $6x-9y=1$
In order to solve the system of equations, we can now subtract equation 1) from equation 2):
$6x-9y-(6x-9y)=3-2$
$0=1$
This means that the system of equations is inconsistent; there is no real solution to it.
Graphing both equations we can observe that they don't intersect. See the picture attached.