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Which describes the system of equations below?\newliney=−x+10y = -x + 10\newliney=−58x−45y = -\frac{5}{8}x - \frac{4}{5}\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=−x+10y = -x + 10\newliney=−58x−45y = -\frac{5}{8}x - \frac{4}{5}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and dependent\newline(C)consistent and independent
  1. Analyze Slopes: Analyze the slopes of both equations.\newlineThe first equation is y=−x+10y = -x + 10, which has a slope of −1-1.\newlineThe second equation is y=−58x−45y = -\frac{5}{8}x - \frac{4}{5}, which has a slope of −58-\frac{5}{8}.\newlineSince the slopes are different (−1≠−58-1 \neq -\frac{5}{8}), the lines are not parallel and will intersect at one point.
  2. Single Solution: Determine if the system has a single solution.\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.
  3. Dependent or Independent: Determine if the system is dependent or independent. Because the lines intersect at exactly one point, they are not the same line, and thus the system is independent.

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