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How many solutions does the system of equations below have?\newliney=14x−9y = \frac{1}{4}x - 9\newliney=14x−107y = \frac{1}{4}x - \frac{10}{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=14x−9y = \frac{1}{4}x - 9\newliney=14x−107y = \frac{1}{4}x - \frac{10}{7}\newlineChoices:\newline(A) no solution\newline(B) one solution\newline(C) infinitely many solutions
  1. Analyze Equations: Step 11: Analyze the equations given.\newliney=14x−9y = \frac{1}{4}x - 9\newliney=14x−107y = \frac{1}{4}x - \frac{10}{7}\newlineBoth equations have the same slope (14\frac{1}{4}), which means they are parallel lines.
  2. Check Y-Intercepts: Step 22: Check the y-intercepts.\newlineThe y-intercepts are different: −9-9 and −107-\frac{10}{7}. Since the slopes are the same and the y-intercepts are different, the lines never intersect.
  3. Conclude Number of Solutions: Step 33: Conclude the number of solutions. Parallel lines with different yy-intercepts do not meet; hence, there are no solutions to the system.

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