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Which describes the system of equations below?\newliney=45x+4y = \frac{4}{5}x + 4\newliney=−310x−310y = -\frac{3}{10}x - \frac{3}{10}\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=45x+4y = \frac{4}{5}x + 4\newliney=−310x−310y = -\frac{3}{10}x - \frac{3}{10}\newlineChoices:\newline(A)consistent and independent\newline(B)inconsistent\newline(C)consistent and dependent
  1. Identify slopes of equations: We have the system of equations:\newliney=45x+4y = \frac{4}{5}x + 4\newliney=−310x−310y = \frac{-3}{10}x - \frac{3}{10}\newlineIdentify whether the slopes of both the equations are the same.\newlineIn y=45x+4y = \frac{4}{5}x + 4, the slope is 45\frac{4}{5}.\newlineIn y=−310x−310y = \frac{-3}{10}x - \frac{3}{10}, the slope is −310\frac{-3}{10}.\newlineNo, the slopes of both the equations are not the same.
  2. Determine if slopes are same: Since the slopes of the two equations are different, this means that the lines will intersect at exactly one point. This implies that the system of equations has a unique solution.\newlineTherefore, the system of equations is consistent and independent.

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