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How many solutions does the system of equations below have?\newliney=−7x+9y = -7x + 9\newliney=97x−74y = \frac{9}{7}x - \frac{7}{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=−7x+9y = -7x + 9\newliney=97x−74y = \frac{9}{7}x - \frac{7}{4}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes: Analyze the slopes of both equations.\newlineEquation 11: y=−7x+9y = -7x + 9, slope = −7-7.\newlineEquation 22: y=97x−74y = \frac{9}{7}x - \frac{7}{4}, slope = 97\frac{9}{7}.\newlineCheck if slopes are equal or different.
  2. Check slopes: Since the slopes are different (−7≠97-7 \neq \frac{9}{7}), the lines are not parallel and will intersect at one point.\newlineDetermine the number of solutions when lines intersect.

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