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How many solutions does the system of equations below have?\newliney=7x6y = 7x - 6\newliney=7x6y = 7x - 6\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=7x6y = 7x - 6\newliney=7x6y = 7x - 6\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=7x6y = 7x − 6\newliney=7x6y = 7x − 6\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. Common Solutions: This means that any point (x,y)(x, y) that lies on the line y=7x6y = 7x - 6 will satisfy both equations simultaneously.
  4. Infinite Solutions: Therefore, the system of equations does not have a unique solution. Instead, it has infinitely many solutions because the lines represented by the equations are the same line, and thus they intersect at all points on that line.

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