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Which describes the system of equations below?\newliney=34x+7y = \frac{3}{4}x + 7\newliney=34x+7y = \frac{3}{4}x + 7\newlineChoices:\newline(A)inconsistent\newline(B)consistent and independent\newline(C)consistent and dependent

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Q. Which describes the system of equations below?\newliney=34x+7y = \frac{3}{4}x + 7\newliney=34x+7y = \frac{3}{4}x + 7\newlineChoices:\newline(A)inconsistent\newline(B)consistent and independent\newline(C)consistent and dependent
  1. Determine Equation Relationship: 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.
  2. Identify Identical Equations: Both equations are y=34x+7y = \frac{3}{4}x + 7. This means that every solution to the first equation is also a solution to the second equation. They are the same line.
  3. Infinite Solutions: Since the two equations are identical, they have infinitely many solutions in common. This means that any point that lies on the first line also lies on the second line.
  4. Dependent System: A system of equations that has infinitely many solutions is called a dependent system because the second equation depends on the first (or vice versa).
  5. Correct System Description: Therefore, the correct description of the system of equations is (C)(C) consistent and dependent.

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