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How many solutions does the system of equations below have?\newliney=−7x+2y = -7x + 2\newliney=35x+57y = \frac{3}{5}x + \frac{5}{7}\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=−7x+2y = -7x + 2\newliney=35x+57y = \frac{3}{5}x + \frac{5}{7}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze Slopes: Analyze the slopes of the two equations.\newlineThe slope of the first equation y=−7x+2y = -7x + 2 is −7-7.\newlineThe slope of the second equation y=35x+57y = \frac{3}{5}x + \frac{5}{7} is 35\frac{3}{5}.\newlineSince the slopes are different, the lines are not parallel.
  2. Identify Intersection Point: Since the slopes are different, the lines will intersect at exactly one point. This means there is one unique solution to the system of equations.

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