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Which describes the system of equations below?\newliney=−8x+8y = -8x + 8\newliney=−95x+94y = -\frac{9}{5}x + \frac{9}{4}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent

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Q. Which describes the system of equations below?\newliney=−8x+8y = -8x + 8\newliney=−95x+94y = -\frac{9}{5}x + \frac{9}{4}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent
  1. Analyze System Type: Analyze the given system of equations to determine its type.\newlineWe have two equations:\newliney=−8x+8y = -8x + 8 (Equation 11)\newliney=−95x+94y = -\frac{9}{5}x + \frac{9}{4} (Equation 22)\newlineTo determine if the system is consistent and dependent, consistent and independent, or inconsistent, we need to compare the slopes and y-intercepts of the two lines represented by these equations.
  2. Compare Slopes: Compare the slopes of the two equations.\newlineThe slope of Equation 11 is −8-8.\newlineThe slope of Equation 22 is −95-\frac{9}{5}.\newlineSince the slopes are different (−8≠−95-8 \neq -\frac{9}{5}), the lines are not parallel and therefore they are not consistent and dependent.
  3. Determine Consistency: Determine if the system is inconsistent or consistent and independent.\newlineSince the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent and independent.

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