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How many solutions does the system of equations below have?\newliney=7x+10y = 7x + 10\newliney=67x+75y = \frac{6}{7}x + \frac{7}{5}\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+10y = 7x + 10\newliney=67x+75y = \frac{6}{7}x + \frac{7}{5}\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=7x+10y = 7x + 10 is 77.\newlineThe slope of the second equation y=67x+75y = \frac{6}{7}x + \frac{7}{5} is 67\frac{6}{7}.\newlineSince the slopes are different, the lines are not parallel.
  2. 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.
  3. Unique solution: There is no need to find the exact point of intersection since we are only asked about the number of solutions. We have determined that there is one solution based on the slopes being different.

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