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Which describes the system of equations below?\newliney=−5x−8y = -5x - 8\newliney=−5x−74y = -5x - \frac{7}{4}\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=−5x−8y = -5x - 8\newliney=−5x−74y = -5x - \frac{7}{4}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent
  1. Compare slopes: Compare the slopes of both equations.\newliney=−5x−8y = -5x - 8 has a slope of −5-5.\newliney=−5x−74y = -5x - \frac{7}{4} also has a slope of −5-5.\newlineSince both slopes are the same, the lines are either parallel or the same line.
  2. Compare y-intercepts: Compare the y-intercepts of both equations.\newliney=−5x−8y = -5x - 8 has a y-intercept of −8-8.\newliney=−5x−74y = -5x - \frac{7}{4} has a y-intercept of −74-\frac{7}{4}.\newlineSince the y-intercepts are different, the lines are parallel and do not intersect.
  3. Determine system type: Determine the type of system based on the slopes and yy-intercepts.\newlineSince the lines are parallel and have different yy-intercepts, they never meet. This means the system is inconsistent.

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