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How many solutions does the system of equations below have?\newliney=−7x−3y = -7x - 3\newliney=45x+18y = \frac{4}{5}x + \frac{1}{8}\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−3y = -7x - 3\newliney=45x+18y = \frac{4}{5}x + \frac{1}{8}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze Slopes: Analyze the slopes of both equations to determine if they are the same or different.\newlineThe slope of the first equation y=−7x−3y = -7x - 3 is −7-7.\newlineThe slope of the second equation y=45x+18y = \frac{4}{5}x + \frac{1}{8} is 45\frac{4}{5}.\newlineSince −7-7 is not equal to 45\frac{4}{5}, the slopes of the equations are different.
  2. Determine Different Slopes: Since the slopes are different, the lines are not parallel and will intersect at exactly one point.\newlineThis means the system of equations has one unique solution.

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