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Which describes the system of equations below?\newliney=27x−27y = \frac{2}{7}x - \frac{2}{7}\newliney=27x+12y = \frac{2}{7}x + \frac{1}{2}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent

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Q. Which describes the system of equations below?\newliney=27x−27y = \frac{2}{7}x - \frac{2}{7}\newliney=27x+12y = \frac{2}{7}x + \frac{1}{2}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent
  1. Analyze Relationship: Analyze the given system of equations to determine their relationship.\newlineThe system of equations is:\newliney=27x−27y = \frac{2}{7}x − \frac{2}{7}\newliney=27x+12y = \frac{2}{7}x + \frac{1}{2}\newlineBoth equations have the same slope (27\frac{2}{7}), but different y-intercepts (−27−\frac{2}{7} and 12\frac{1}{2}, respectively). This means that the lines are parallel and will never intersect.
  2. Determine System Type: Determine the type of system based on the analysis.\newlineSince the lines are parallel and have different yy-intercepts, there is no point that satisfies both equations simultaneously. Therefore, the system has no solution.
  3. Match Conclusion: Match the conclusion from Step 22 with the correct choice.\newlineA system with no solution is considered inconsistent because there are no points where the equations intersect.

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