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Which describes the system of equations below?\newliney=38x+74y = \frac{3}{8}x + \frac{7}{4}\newliney=38x−29y = \frac{3}{8}x - \frac{2}{9}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent\newline

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Q. Which describes the system of equations below?\newliney=38x+74y = \frac{3}{8}x + \frac{7}{4}\newliney=38x−29y = \frac{3}{8}x - \frac{2}{9}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent\newline
  1. Identify slopes and y-intercepts: Analyze the equations to identify their slopes and y-intercepts.\newlineEquation 11: y=38x+74y = \frac{3}{8}x + \frac{7}{4}\newlineEquation 22: y=38x−29y = \frac{3}{8}x - \frac{2}{9}\newlineBoth equations have the same slope (38\frac{3}{8}), but different y-intercepts (74\frac{7}{4} and −29-\frac{2}{9}).
  2. Determine relationship based on slopes and y-intercepts: Determine the relationship between the equations based on their slopes and y-intercepts.\newlineSince the slopes are identical but the y-intercepts are different, the lines are parallel and never intersect.
  3. Conclude system type: Conclude the type of system they form. Parallel lines with the same slope mm and different yy-intercepts mean the system is inconsistent; there are no points of intersection.

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