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Which describes the system of equations below?\newliney=x+2y = x + 2\newliney=310x−23y = \frac{3}{10}x - \frac{2}{3}\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=x+2y = x + 2\newliney=310x−23y = \frac{3}{10}x - \frac{2}{3}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent
  1. Identify slopes of equations: We have the system of equations:\newliney=x+2y = x + 2\newliney=310x−23y = \frac{3}{10}x - \frac{2}{3}\newlineIdentify whether the slopes of both the equations are the same.\newlineIn y=x+2y = x + 2, the slope is 11.\newlineIn y=310x−23y = \frac{3}{10}x - \frac{2}{3}, the slope is 310\frac{3}{10}.\newlineNo, the slopes of both the equations are not the same.
  2. Determine if slopes are same: Since the slopes are different, the lines are not parallel and will intersect at exactly one point. This means the system of equations has one unique solution. Therefore, the system of equations is consistent and independent.

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