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How many solutions does the system of equations below have?\newliney=47x−7y = \frac{4}{7}x - 7\newliney=−89x+87y = -\frac{8}{9}x + \frac{8}{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=47x−7y = \frac{4}{7}x - 7\newliney=−89x+87y = -\frac{8}{9}x + \frac{8}{7}\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=47x−7y = \frac{4}{7}x - 7 is 47\frac{4}{7}.\newlineThe slope of the second equation y=−89x+87y = -\frac{8}{9}x + \frac{8}{7} is −89-\frac{8}{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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