Question

Is the system of equations consistent, consistent and coincident, or inconsistent?

Answer 1

Here, Your equations are:
y = 3x + 4
y = 3x + 3

Compare both the sides, 
3x + 4 = 3x + 3
3x - 3x = 4 - 3
0 ≠ 1
As zero can't be equal to 1, the equation has no solution

In short, Your Answer would be "Inconsistent"

Hope this helps!