System A Line 1: $y=x+1$ Line 2: $y=x-4$ This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: $(\square, \square)$ infinitely many solutions no solution

Step 1 ：The system of equations is a set of two linear equations. To find out whether the system is inconsistent, consistent dependent, or consistent independent, we need to check the slopes and y-intercepts of the two lines. If the slopes are equal and the y-intercepts are different, the system is inconsistent (no solution). If the slopes and y-intercepts are equal, the system is consistent dependent (infinitely many solutions). If the slopes are different, the system is consistent independent (a unique solution).

Step 2 ：Calculate the slope and y-intercept for Line 1: \(y=x+1\). The slope is 1 and the y-intercept is 1.

Step 3 ：Calculate the slope and y-intercept for Line 2: \(y=x-4\). The slope is 1 and the y-intercept is -4.

Step 4 ：The slopes of the two lines are equal and the y-intercepts are different. Therefore, the system is inconsistent and has no solution.

Step 5 ：Final Answer: The system is \(\boxed{\text{inconsistent}}\) and has \(\boxed{\text{no solution}}\).