Final answer:
The system of equations y=2x-1 and y=-2x+5 is independent because the lines have opposite slopes and different y-intercepts, meaning they intersect at one point.
Step-by-step explanation:
The system of equations described by y=2x-1 and y=-2x+5 can be classified by comparing their slopes and y-intercepts. Since the slopes of the two lines are opposites (2 and -2) and the y-intercepts are different (-1 and 5), these lines will intersect at exactly one point. This means they are independent; each equation represents a straight line, and the system has a single solution where these two lines cross.
In the context of this question, the independent variable is x (which can be chosen freely), and the dependent variable is y (which depends on the value of x through the equation of the line).