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Which describes the system of equations below?\newliney=10x+5y = 10x + 5\newliney=10x−56y = 10x - \frac{5}{6}\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=10x+5y = 10x + 5\newliney=10x−56y = 10x - \frac{5}{6}\newlineChoices:\newline(A)consistent and independent\newline(B)inconsistent\newline(C)consistent and dependent
  1. Compare slopes: Compare the slopes of both equations.\newliney=10x+5y = 10x + 5 has a slope of 1010.\newliney=10x−56y = 10x - \frac{5}{6} also has a slope of 1010.\newlineSince both slopes are the same, the lines are either parallel or the same line.
  2. Compare y-intercepts: Compare the y-intercepts of both equations.\newliney=10x+5y = 10x + 5 has a y-intercept of 55.\newliney=10x−56y = 10x - \frac{5}{6} has a y-intercept of −56-\frac{5}{6}.\newlineSince the y-intercepts are different, the lines are parallel and do not intersect.

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