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Which describes the system of equations below?\newliney=2x−75y = 2x - \frac{7}{5}\newliney=83x+85y = \frac{8}{3}x + \frac{8}{5}\newlineChoices:\newline(A)consistent and independent\newline(B)inconsistent\newline(C)consistent and dependent

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Q. Which describes the system of equations below?\newliney=2x−75y = 2x - \frac{7}{5}\newliney=83x+85y = \frac{8}{3}x + \frac{8}{5}\newlineChoices:\newline(A)consistent and independent\newline(B)inconsistent\newline(C)consistent and dependent
  1. Analyze System of Equations: Analyze the given system of equations to determine its type.\newlineWe have two equations:\newliney=2x−75y = 2x − \frac{7}{5}\newliney=83x+85y = \frac{8}{3}x + \frac{8}{5}\newlineTo determine if the system is consistent and independent, inconsistent, or consistent and dependent, we need to compare the slopes and yy-intercepts of the two lines represented by these equations.
  2. Compare Slopes: Compare the slopes of the two equations.\newlineThe slope of the first equation y=2x−75y = 2x - \frac{7}{5} is 22.\newlineThe slope of the second equation y=83x+85y = \frac{8}{3}x + \frac{8}{5} is 83\frac{8}{3}.\newlineSince the slopes are different 2≠832 \neq \frac{8}{3}, the lines are not parallel and therefore they will intersect at exactly one point.\newlineThis means the system is consistent and has a unique solution.
  3. Determine Consistency: Since the slopes are different, we do not need to compare the yy-intercepts to determine the type of system.\newlineThe system is consistent and independent because the lines will intersect at exactly one point.

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