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How many solutions does the system of equations below have?\newliney=−49x+72y = -\frac{4}{9}x + \frac{7}{2}\newliney=−49x+57y = -\frac{4}{9}x + \frac{5}{7}\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=−49x+72y = -\frac{4}{9}x + \frac{7}{2}\newliney=−49x+57y = -\frac{4}{9}x + \frac{5}{7}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Compare slopes: Compare the slopes of both equations.\newlineSlope of first equation: −49-\frac{4}{9}\newlineSlope of second equation: −49-\frac{4}{9}\newlineSince both slopes are the same, the lines are parallel or identical.
  2. Compare y-intercepts: Compare the y-intercepts of both equations.\newliney-intercept of first equation: 72\frac{7}{2}\newliney-intercept of second equation: 57\frac{5}{7}\newlineSince the y-intercepts are different, the lines are parallel and do not intersect.

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