Hello, jvignacio!
Your work is correct!
Here's another approach . . .
I tried to solve this two equations using substitution
but my x's ended up canceling out when trying to solve for x.
$\displaystyle \begin{array}{cccc}6x  2y &=& 14 & [1] \\
\text{}9x + 3y &=& 12 & [2] \end{array}$
Graphic solution: we want the intersection of the two lines.
$\displaystyle \begin{array}{cc}\text{Solve [1] for }y\!: & y\:=\:3x  7 \\
\text{Solve [2] for }y\!: & y\:=\:3x + 4 \end{array}$
We have two lines: one has yintercept 7, the other has yintercept 4.
Both have slope 3 . . . The lines are parallel. Code:
 /
/ /
4* /
/ /
/  /
/+/
/ /
7*
/
/ 

Obviously, the line do not intersect.
Therefore, the system has no solution.