Q. Which describes the system of equations below?y=7x−1y=7x+52Choices:(A)inconsistent(B)consistent and independent(C)consistent and dependent
Identify slopes: We have the following system of equations:y=7x−1y=7x+52Identify whether the slopes of both the equations are the same.In y=7x−1, the slope is 7.In y=7x+52, the slope is also 7.Yes, the slopes of both equations are the same.
Identify y-intercepts: Now, identify whether the y-intercepts of both equations are the same.In y=7x−1, the y-intercept is −1.In y=7x+52, the y-intercept is 52.No, the y-intercepts of both equations are not the same.
Determine inconsistency: Since the slopes of the equations are the same but the y-intercepts are different, the lines are parallel to each other and will never intersect.This means that there is no solution to the system of equations, and the system is inconsistent.