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Which describes the system of equations below?\newliney=47x−23y = \frac{4}{7}x - \frac{2}{3}\newliney=47x−910y = \frac{4}{7}x - \frac{9}{10}\newlineChoices:\newline(A)consistent and independent\newline(B)inconsistent\newline(C)consistent and dependent

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Q. Which describes the system of equations below?\newliney=47x−23y = \frac{4}{7}x - \frac{2}{3}\newliney=47x−910y = \frac{4}{7}x - \frac{9}{10}\newlineChoices:\newline(A)consistent and independent\newline(B)inconsistent\newline(C)consistent and dependent
  1. Analyze Equations: Analyze the given system of equations to determine their relationship.\newlineThe system of equations is:\newliney=47x−23y = \frac{4}{7}x − \frac{2}{3}\newliney=47x−910y = \frac{4}{7}x − \frac{9}{10}\newlineBoth equations have the same slope (47\frac{4}{7}) but different y-intercepts (−23−\frac{2}{3} and −910−\frac{9}{10}). This means that the lines are parallel to each other.
  2. Determine Relationship: Determine the type of system based on the analysis.\newlineSince the lines are parallel and have different yy-intercepts, they will never intersect. Therefore, there are no points that satisfy both equations simultaneously.
  3. System Type: Choose the correct description from the given choices based on the analysis.\newline(A) Consistent and independent systems have one solution, which means the lines intersect at exactly one point. This is not our case.\newline(B) Inconsistent systems have no solution, which means the lines are parallel and do not intersect. This is our case.\newline(C) Consistent and dependent systems have infinitely many solutions, which means the lines are coincident (the same line). This is not our case.

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