Answer:
[tex]\displaystyle Inconsistency\:[No\:Solution][/tex]
Step-by-step explanation:
We need to isolate one pair of variables so they are set to zero. Now, in this case, we need to split one of the equations in negative half, so we will select the second equation:
[tex]\displaystyle \left \{ {{3x - 2y = 8} \atop {6x - 4y = 12}} \right. \\ \\ \\ \left \{ {{3x - 2y = 8} \atop {-\frac{1}{2}[6x - 4y = 12]}} \right. \\ \\ \left \{ {{3x - 2y = 8} \atop {-3x + 2y = -6}} \right. \\ \\ \\ \boxed{0 \ne 2}[/tex]
The fact that we have a result like this proves that we cannot obtain a solution from this system, which means that on a graph, these equations are considered parallel [no intersection, so no solution].
I am joyous to assist you at any time.
