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Which describes the system of equations below?\newliney=6x−2y = 6x - 2\newliney=6x−2y = 6x - 2\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent

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Q. Which describes the system of equations below?\newliney=6x−2y = 6x - 2\newliney=6x−2y = 6x - 2\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent
  1. Compare Equations: To determine the type of system the two equations represent, we need to compare the equations to see if they are the same, parallel, or intersect at a single point.\newliney=6x−2y = 6x − 2\newliney=6x−2y = 6x − 2\newlineWe can see that both equations are identical.
  2. Identical Equations: Since both equations are identical, they represent the same line. Therefore, every point on the line y=6x−2y = 6x - 2 is a solution to the system of equations. This means that there are an infinite number of solutions.
  3. Consistent and Dependent System: A system of equations with an infinite number of solutions is known as a consistent and dependent system. This is because the equations are consistent (they have at least one solution) and dependent (they are essentially the same line, so all solutions of one equation are also solutions of the other).

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