Question

what is the correct classification of the systems of equations y-4x=-3 & 12x-3y=9

Answer 1

divide the second equation of your system by -3 and you will see that the equations are same.

Answer 2

So they're parallel?

Answer 3

Yes, they are parallel.
And that means that how many solutions do they have?

Answer 4

1?

Answer 5

The rule is that if the lines are parallel, then they have no solutions, because parallel lines NEVER intersect with each other. (And the solution of the system of equation is the intersection point(s) ).