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Which describes the system of equations below?\newliney=75x+34y = \frac{7}{5}x + \frac{3}{4}\newliney=75x+34y = \frac{7}{5}x + \frac{3}{4}\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=75x+34y = \frac{7}{5}x + \frac{3}{4}\newliney=75x+34y = \frac{7}{5}x + \frac{3}{4}\newlineChoices:\newline(A) inconsistent\newline(B) consistent and independent\newline(C) consistent and dependent
  1. Analyze System of Equations: Analyze the given system of equations.\newlineThe system of equations is:\newliney=75x+34y = \frac{7}{5}x + \frac{3}{4}\newliney=75x+34y = \frac{7}{5}x + \frac{3}{4}\newlineWe notice that both equations are identical.
  2. Determine Nature of System: 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 there are infinitely many solutions, and the lines represented by these equations would lie on top of each other on a graph.
  3. Classify Based on Solutions: Classify the system based on the number of solutions. A system of equations that has infinitely many solutions is called ＂consistent and dependent＂ because the equations depend on each other to have the same graph.

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