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Which describes the system of equations below?\newliney=6x+25y = 6x + \frac{2}{5}\newliney=27x+83y = \frac{2}{7}x + \frac{8}{3}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent

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Q. Which describes the system of equations below?\newliney=6x+25y = 6x + \frac{2}{5}\newliney=27x+83y = \frac{2}{7}x + \frac{8}{3}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent
  1. Identify slopes: Step 11: Identify the slopes of both equations.\newlineFor y=6x+25y = 6x + \frac{2}{5}, the slope is 66.\newlineFor y=27x+83y = \frac{2}{7}x + \frac{8}{3}, the slope is 27\frac{2}{7}.\newlineSince the slopes are different, the lines are not parallel and will intersect at one point.
  2. Check y-intercepts: Step 22: Check if the y-intercepts are the same.\newlineFor y=6x+25y = 6x + \frac{2}{5}, the y-intercept is 25\frac{2}{5}.\newlineFor y=27x+83y = \frac{2}{7}x + \frac{8}{3}, the y-intercept is 83\frac{8}{3}.\newlineThe y-intercepts are different, confirming that the lines will intersect at one point.

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