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Which describes the system of equations below?Choices:(A)consistent and independent(B)consistent and dependent(C)inconsistent
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Q. Which describes the system of equations below?Choices:(A)consistent and independent(B)consistent and dependent(C)inconsistent
- Compare Slopes: We have the system of equations:First, we need to compare the slopes of both equations.In , the slope is .In , the slope is also .Since the slopes are the same, we can say that the lines are either parallel or the same line.
- Compare Y-Intercepts: Next, we compare the y-intercepts of both equations.In , the y-intercept is .In , the y-intercept is also .Since the y-intercepts are the same, we can conclude that the lines are not just parallel, but they are in fact the same line.
- Conclusion: Since both the slope and -intercept of the two equations are the same, the system of equations represents the same line. Therefore, any solution that lies on one line will also lie on the other, meaning there are infinitely many solutions.This means the system of equations is consistent because there are solutions, and it is dependent because the equations describe the same line and thus have all their solutions in common.
