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How many solutions does the system of equations below have?\newliney=7x−27y = 7x - \frac{2}{7}\newliney=58x−67y = \frac{5}{8}x - \frac{6}{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−27y = 7x - \frac{2}{7}\newliney=58x−67y = \frac{5}{8}x - \frac{6}{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−27y = 7x − \frac{2}{7} is 77.\newlineThe slope of the second equation y=58x−67y = \frac{5}{8}x − \frac{6}{7} is 58\frac{5}{8}.\newlineSince the slopes are different, the lines are not parallel.
  2. Unique Solution: 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.
  3. No YY-intercept Check: There is no need to check the yy-intercepts because the slopes are different, which guarantees that the lines will intersect at some point.

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