Final answer:
The given system has no solutions because the lines are parallel.
Step-by-step explanation:
The given system of equations is:
y = 3x + 12
y = 3x - 10
To find the number of solutions, we need to compare the slopes of the two equations. Since both equations have the same slope, which is 3, the lines are parallel. Parallel lines do not intersect and therefore do not have any solutions. So, the correct answer is option 2. No solutions, the lines are parallel.