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Which describes the system of equations below?\newliney=310x+6y = \frac{3}{10}x + 6\newliney=310x−25y = \frac{3}{10}x - \frac{2}{5}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and independent\newline(C)consistent and dependent

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Q. Which describes the system of equations below?\newliney=310x+6y = \frac{3}{10}x + 6\newliney=310x−25y = \frac{3}{10}x - \frac{2}{5}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and independent\newline(C)consistent and dependent
  1. Compare slopes: Step 11: Compare the slopes of both equations.\newlineEquation 11: y=310x+6y = \frac{3}{10}x + 6, slope = 310\frac{3}{10}.\newlineEquation 22: y=310x−25y = \frac{3}{10}x - \frac{2}{5}, slope = 310\frac{3}{10}.\newlineSince both slopes are the same, the lines are either parallel or the same line.
  2. Compare y-intercepts: Step 22: Compare the y-intercepts of both equations.\newlineEquation 11: y=310x+6y = \frac{3}{10}x + 6, y-intercept = 66.\newlineEquation 22: y=310x−25y = \frac{3}{10}x - \frac{2}{5}, y-intercept = −25-\frac{2}{5}.\newlineSince the y-intercepts are different, the lines are parallel and do not intersect.

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