Answer
$C$
Work Step by Step
In this case, we first want to modify the equations so that one of the variable terms is the same in both equations but differing in sign. Multiply the first equation by $-2$:
$-6x + 8y = -24$
Set up the system of equations using this modified equation above:
$-6x + 8y = -24$
$6x - 8y = 12$
Add the equations together:
$(-6x + 8y)+(6x - 8y) = -24+12
0 = -12$
This statement is false; therefore, this system of equations has no solution.
The lines never meet at any point, so the lines are parallel.
This corresponds to option $C$.
