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Which describes the system of equations below?\newliney=13x+97y = \frac{1}{3}x + \frac{9}{7}\newliney=13x+97y = \frac{1}{3}x + \frac{9}{7}\newlineChoices:\newline(A) inconsistent\newline(B) consistent and independent\newline(C) consistent and dependent

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Q. Which describes the system of equations below?\newliney=13x+97y = \frac{1}{3}x + \frac{9}{7}\newliney=13x+97y = \frac{1}{3}x + \frac{9}{7}\newlineChoices:\newline(A) inconsistent\newline(B) consistent and independent\newline(C) consistent and dependent
  1. Analyze the system: Analyze the given system of equations.\newlineWe have two equations:\newliney=13x+97y = \frac{1}{3}x + \frac{9}{7}\newliney=13x+97y = \frac{1}{3}x + \frac{9}{7}\newlineWe notice that both equations are identical.
  2. Determine nature: Determine the nature of the system.\newlineSince both equations are the same, every solution to the first equation is also a solution to the second equation. This means that the lines represented by these equations would lie on top of each other on a graph, indicating that there are infinitely many solutions.
  3. Classify based on solutions: Classify the system based on the number of solutions. A system of equations that has infinitely many solutions is known as a consistent and dependent system because the two equations describe the same line.

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