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Which describes the system of equations below?\newliney=−29x+43y = -\frac{2}{9}x + \frac{4}{3}\newliney=−29x+43y = -\frac{2}{9}x + \frac{4}{3}\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent

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Q. Which describes the system of equations below?\newliney=−29x+43y = -\frac{2}{9}x + \frac{4}{3}\newliney=−29x+43y = -\frac{2}{9}x + \frac{4}{3}\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent
  1. Analyze Equations: Analyze the given system of equations to determine their relationship.\newlineThe system of equations is:\newliney=−29x+43y = \frac{-2}{9}x + \frac{4}{3}\newliney=−29x+43y = \frac{-2}{9}x + \frac{4}{3}\newlineWe can see that both equations are identical.
  2. Determine System Type: Determine the type of system based on the equations.\newlineSince both equations are the same, every solution that works for one equation will also work for the other. This means that the system has infinitely many solutions.
  3. Match with Description: Match the system with the correct description based on the number of solutions. A system with infinitely many solutions is considered consistent because there are solutions, and dependent because all solutions are shared between the equations.

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