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How many solutions does the system of equations below have?\newliney=−29x+65y = -\frac{2}{9}x + \frac{6}{5}\newliney=56x+87y = \frac{5}{6}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=−29x+65y = -\frac{2}{9}x + \frac{6}{5}\newliney=56x+87y = \frac{5}{6}x + \frac{8}{7}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Identify slopes: Identify the slopes of each equation.\newliney=−29x+65y = \frac{-2}{9}x + \frac{6}{5} has a slope of −29\frac{-2}{9}.\newliney=56x+87y = \frac{5}{6}x + \frac{8}{7} has a slope of 56\frac{5}{6}.\newlineSince the slopes are different, the lines are not parallel and not the same line.
  2. Check intersection: Check if the lines intersect.\newlineDifferent slopes mean the lines will intersect at exactly one point.

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