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How many solutions does the system of equations below have?\newliney=8x−8y = 8x - 8\newliney=73x+54y = \frac{7}{3}x + \frac{5}{4}\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=8x−8y = 8x - 8\newliney=73x+54y = \frac{7}{3}x + \frac{5}{4}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes of equations: Analyze the slopes of the two equations.\newlineThe slope of the first equation y=8x−8y = 8x − 8 is 88.\newlineThe slope of the second equation y=73x+54y = \frac{7}{3}x + \frac{5}{4} is 73\frac{7}{3}.\newlineSince the slopes are different (8≠738 \neq \frac{7}{3}), the lines are not parallel.
  2. Slopes determine intersection: 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.

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