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How many solutions does the system of equations below have?\newliney=73x−53y = \frac{7}{3}x - \frac{5}{3}\newliney=107x+710y = \frac{10}{7}x + \frac{7}{10}\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=73x−53y = \frac{7}{3}x - \frac{5}{3}\newliney=107x+710y = \frac{10}{7}x + \frac{7}{10}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes of equations: Analyze the slopes of both equations.\newlineThe slope of the first equation y=73x−53y = \frac{7}{3}x - \frac{5}{3} is 73\frac{7}{3}.\newlineThe slope of the second equation y=107x+710y = \frac{10}{7}x + \frac{7}{10} is 107\frac{10}{7}.\newlineSince the slopes are different 73≠107\frac{7}{3} \neq \frac{10}{7}, the lines are not parallel.
  2. Identify different slopes: 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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