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Which describes the system of equations below?\newliney=4x+6y = 4x + 6\newliney=4x+73y = 4x + \frac{7}{3}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and dependent\newline(C)consistent and independent

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Q. Which describes the system of equations below?\newliney=4x+6y = 4x + 6\newliney=4x+73y = 4x + \frac{7}{3}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and dependent\newline(C)consistent and independent
  1. Determine System Type: To determine the type of system the two equations represent, we need to compare the slopes and y-intercepts of the equations.\newlineThe first equation is y=4x+6y = 4x + 6, which has a slope of 44 and a y-intercept of 66.\newlineThe second equation is y=4x+73y = 4x + \frac{7}{3}, which also has a slope of 44 but a different y-intercept of 73\frac{7}{3}.\newlineSince both lines have the same slope but different y-intercepts, they are parallel and will never intersect.
  2. Compare Equations: A system of equations that has parallel lines with no points of intersection is considered inconsistent because there are no solutions that satisfy both equations simultaneously.

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