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How many solutions does the system of equations below have?\newliney=19x+75y = \frac{1}{9}x + \frac{7}{5}\newliney=−34x+59y = -\frac{3}{4}x + \frac{5}{9}\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=19x+75y = \frac{1}{9}x + \frac{7}{5}\newliney=−34x+59y = -\frac{3}{4}x + \frac{5}{9}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes: Analyze the slopes of both equations to determine if they are the same or different.\newlineEquation 11: y=19x+75y = \frac{1}{9}x + \frac{7}{5}, Slope = 19\frac{1}{9}.\newlineEquation 22: y=−34x+59y = -\frac{3}{4}x + \frac{5}{9}, Slope = −34-\frac{3}{4}.\newlineSince the slopes are different, the lines are not parallel.
  2. Determine intersection point: Since the slopes are different, the lines must intersect at exactly one point. This means there is one solution to the system of equations.

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