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Which describes the system of equations below?\newliney=7x−6y = 7x - 6\newliney=−45x+29y = -\frac{4}{5}x + \frac{2}{9}\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent

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Q. Which describes the system of equations below?\newliney=7x−6y = 7x - 6\newliney=−45x+29y = -\frac{4}{5}x + \frac{2}{9}\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent
  1. Analyze Equations: Analyze the given system of equations to determine its type.\newlineWe have two equations:\newliney=7x−6y = 7x − 6 (Equation 11)\newliney=−45x+29y = −\frac{4}{5}x + \frac{2}{9} (Equation 22)\newlineTo determine if the system is consistent and independent, consistent and dependent, or inconsistent, we need to look at the slopes and yy-intercepts of the two lines represented by these equations.
  2. Compare Slopes: Compare the slopes of the two lines.\newlineThe slope of Equation 11 is 77, and the slope of Equation 22 is −45-\frac{4}{5}. Since the slopes are different, the lines are not parallel and therefore they must intersect at exactly one point.
  3. Determine Consistency: Determine if the system is consistent and independent, consistent and dependent, or inconsistent.\newlineSince the lines have different slopes and will intersect at exactly one point, the system is consistent and independent. This means there is one unique solution to the system.

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