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How many solutions does the system of equations below have?\newliney=2x1y = 2x - 1\newliney=2x1y = 2x - 1\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

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Q. How many solutions does the system of equations below have?\newliney=2x1y = 2x - 1\newliney=2x1y = 2x - 1\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Given Equations: The system of equations is given as:\newliney=2x1y = 2x − 1\newliney=2x1y = 2x − 1\newlineWe need to determine how many solutions this system has.\newlineSince both equations are identical, every solution to one equation is also a solution to the other. This means that the lines represented by these equations are the same line, and they overlap completely.
  2. Identical Equations: Because the two lines are the same, any point that lies on one line will also lie on the other. Therefore, there are infinitely many points that satisfy both equations simultaneously.
  3. Infinite Solutions: Given the choices (A) no solution, (B) one solution, and (C) infinitely many solutions, the correct choice is (C) infinitely many solutions.

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