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Which describes the system of equations below?\newliney=−9x−58y = -9x - \frac{5}{8}\newliney=−9x−58y = -9x - \frac{5}{8}\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=−9x−58y = -9x - \frac{5}{8}\newliney=−9x−58y = -9x - \frac{5}{8}\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent
  1. Analyze Equations: Analyze the equations to see if they are the same or different.\newlineWe have:\newliney=−9x−58y = -9x - \frac{5}{8}\newliney=−9x−58y = -9x - \frac{5}{8}\newlineBoth equations are identical.
  2. Check Slopes: Check the slopes of both equations.\newlineIn y=−9x−58y = -9x - \frac{5}{8}, the slope is −9-9.\newlineIn y=−9x−58y = -9x - \frac{5}{8}, the slope is also −9-9.\newlineSince both slopes are the same, the lines are parallel or the same line.
  3. Check Y-Intercepts: Check the y-intercepts of both equations.\newlineIn y=−9x−58y = -9x - \frac{5}{8}, the y-intercept is −58-\frac{5}{8}.\newlineIn y=−9x−58y = -9x - \frac{5}{8}, the y-intercept is also −58-\frac{5}{8}.\newlineSince both y-intercepts are the same, the lines are the same line, not just parallel.
  4. Determine System Type: Determine the type of system based on the analysis.\newlineSince both the slope and yy-intercept are the same for both equations, the system is consistent and dependent. They represent the same line, so they have infinitely many solutions.

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