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How many solutions does the system of equations below have?\newliney=−x+5y = -x + 5\newliney=−x+5y = -x + 5\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=−x+5y = -x + 5\newliney=−x+5y = -x + 5\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=−x+5y = -x + 5\newliney=−x+5y = -x + 5\newlineWe need to determine how many solutions this system has.
  2. Identical Equations: Since both equations are identical, every solution to the first equation is also a solution to the second equation.
  3. Overlap of Lines: This means that the lines represented by these equations are the same line, and they overlap completely.
  4. Infinite Solutions: Therefore, there are infinitely many points where the two equations are true, because they are the same line.
  5. Correct Choice: The correct choice that represents the number of solutions for this system of equations is (C)(C) infinitely many solutions.

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