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How many solutions does the system of equations below have?\newliney=−7x−53y = -7x - \frac{5}{3}\newliney=−49x+72y = -\frac{4}{9}x + \frac{7}{2}\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−53y = -7x - \frac{5}{3}\newliney=−49x+72y = -\frac{4}{9}x + \frac{7}{2}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes: Analyze the slopes of both equations.\newlineThe slope of the first equation y=−7x−53y = -7x - \frac{5}{3} is −7-7.\newlineThe slope of the second equation y=−49x+72y = -\frac{4}{9}x + \frac{7}{2} is −49-\frac{4}{9}.\newlineSince the slopes are different, the lines are not parallel.
  2. Determine intersection: Determine if the lines intersect.\newlineBecause the slopes are different, the lines must intersect at exactly one point.\newlineTherefore, the system of equations has one solution.

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