Find the value of k such that the system of equations 2x + 3y = 7 and 6x + ky = 20 has no solution.

Answer and explanation

Correct answer: B. 9

  1. Step 1: A system of linear equations A_1x + B_1y = C_1 and A_2x + B_2y = C_2 has no solution when the lines are parallel but not identical.
  2. Step 2: Parallel condition: A_1 / A_2 = B_1 / B_2 != C_1 / C_2.
  3. Step 3: Ratio of x-coefficients: 2 / 6 = 1/3.
  4. Step 4: Set B_1 / B_2 = 1/3: 3 / k = 1/3, which yields k = 9.
  5. Step 5: Check constants: 7 / 20 != 1/3, confirming that the lines are distinct parallel lines.
Answer
9.
Why not the others: 6 gives ratio 1/2 != 1/3; 12 gives ratio 1/4; 4 gives ratio 3/4.

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