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Which describes the system of equations below?\newliney=−6x−2y = -6x - 2\newliney=94x−49y = \frac{9}{4}x - \frac{4}{9}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and dependent\newline(C)consistent and independent

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Q. Which describes the system of equations below?\newliney=−6x−2y = -6x - 2\newliney=94x−49y = \frac{9}{4}x - \frac{4}{9}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and dependent\newline(C)consistent and independent
  1. Analyze Equations Relationship: Analyze the given system of equations to determine their relationship.\newlineThe system of equations is:\newliney=−6x−2y = -6x - 2\newliney=94x−49y = \frac{9}{4}x - \frac{4}{9}\newlineWe need to check if the lines represented by these equations are parallel, intersecting, or coinciding.
  2. Compare Slopes: Compare the slopes of the two equations.\newlineThe slope of the first equation y=−6x−2y = -6x - 2 is −6-6.\newlineThe slope of the second equation y=94x−49y = \frac{9}{4}x - \frac{4}{9} is 94\frac{9}{4}.\newlineSince the slopes are different, the lines are not parallel and they will intersect at some point.
  3. Determine Solution Type: Determine if the system has one solution or infinitely many solutions.\newlineSince the slopes are different, there is only one point of intersection. This means the system has one solution and is consistent and independent.

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