For which value of does the system of equations have infinitely many solutions?

Answer and explanation

Correct answer: D.

  1. Step 1: For a linear system to have infinitely many solutions, the two equations must be linearly dependent (constant ratio between coefficients).
  2. Step 2: Compute the ratio of coefficients: and .
  3. Step 3: Equate the constant terms using the same ratio: .
Answer
.
Why not the others: '' keeps the constant identical while multiplying the left side by , making the system inconsistent; '' adds 2 to 10; '' multiplies by 2 instead of .

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