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Which describes the system of equations below?\newliney=4x+6y = 4x + 6\newliney=−107x+57y = -\frac{10}{7}x + \frac{5}{7}\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=4x+6y = 4x + 6\newliney=−107x+57y = -\frac{10}{7}x + \frac{5}{7}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent
  1. Analyze slopes: Step 11: Analyze the slopes of both equations.\newlineFor y=4x+6y = 4x + 6, the slope is 44.\newlineFor y=−107x+57y = -\frac{10}{7}x + \frac{5}{7}, the slope is −107-\frac{10}{7}.\newlineSince the slopes are different, the lines are not parallel.
  2. Check intersection: Step 22: Check if the lines intersect.\newlineDifferent slopes imply that the lines will intersect at exactly one point.\newlineThis means the system has one solution.
  3. Determine system type: Step 33: Determine the type of system based on the number of solutions. Since there is exactly one solution, the system is consistent. Also, because they intersect at only one point, the equations are independent.

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