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Which describes the system of equations below?\newliney=−7x−2y = -7x - 2\newliney=25x−27y = \frac{2}{5}x - \frac{2}{7}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent

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Q. Which describes the system of equations below?\newliney=−7x−2y = -7x - 2\newliney=25x−27y = \frac{2}{5}x - \frac{2}{7}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent
  1. Identify Slopes: Identify the slopes of the given equations to determine if they are parallel, the same, or intersecting.\newlineFor the first equation, y=−7x−2y = -7x - 2, the slope (m1m_1) is −7-7.\newlineFor the second equation, y=25x−27y = \frac{2}{5}x - \frac{2}{7}, the slope (m2m_2) is 25\frac{2}{5}.\newlineCheck if m1m_1 equals m2m_2.
  2. Compare Slopes: Compare the slopes.\newlineSince −7-7 is not equal to 25\frac{2}{5}, the lines are not parallel and not the same line.\newlineThis means they must intersect at exactly one point.
  3. Determine System Type: Determine the type of system based on the slopes.\newlineSince the lines intersect at exactly one point, the system is consistent and independent.

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