To determine if the system of equations is consistent and independent, consistent and dependent, or inconsistent, we should first rearrange the equations:
- \( y = 3x + 4 \)
- \( y = 3x + 3 \)
Now, we can set the two equations equal to each other since they both equal \( y \):
\[ 3x + 4 = 3x + 3 \]
Subtracting \( 3x \) from both sides:
\[ 4 = 3 \]
This statement is false, indicating that the two lines represented by the equations are parallel and do not intersect. Therefore, the system of equations is inconsistent.
Answer: Inconsistent