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Which describes the system of equations below?\newliney=x+2y = x + 2\newliney=x−97y = x - \frac{9}{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=x+2y = x + 2\newliney=x−97y = x - \frac{9}{7}\newlineChoices:\newline(A)consistent and dependent\newline(B)consistent and independent\newline(C)inconsistent
  1. Analyze System Characteristics: Analyze the given system of equations to determine its characteristics.\newlineThe system of equations is:\newliney=x+2y = x + 2\newliney=x−97y = x - \frac{9}{7}\newlineTo determine if the system is consistent and dependent, consistent and independent, or inconsistent, we need to compare the slopes and yy-intercepts of the two equations.
  2. Identify Slope and Y-Intercept: Identify the slope and y-intercept of each equation.\newlineFor the first equation, y=x+2y = x + 2, the slope (m)(m) is 11 and the y-intercept (b)(b) is 22.\newlineFor the second equation, y=x−97y = x - \frac{9}{7}, the slope (m)(m) is also 11 and the y-intercept (b)(b) is −97-\frac{9}{7}.
  3. Compare Equations: Compare the slopes and yy-intercepts of the two equations.\newlineSince both equations have the same slope but different yy-intercepts, this means that the lines are parallel and will never intersect.
  4. Determine System Type: Determine the type of system based on the comparison.\newlineBecause the lines are parallel and do not intersect, the system of equations is inconsistent. There is no point that satisfies both equations simultaneously.

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