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