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JEE Main202324 Jan 2023Evening ShiftMathematicsDeterminantsActual

If the system of equations x + 2 y + 3 z = 3 , 4 x + 3 y - 4 z = 4 and 8 x + 4 y - λ z = 9 + μ has infinitely many solutions, then the ordered pair λ , μ is equal to

Options

  1. A72 5 , 21 5
  2. B- 72 5 , - 21 5
  3. C72 5 , - 21 5
  4. D- 72 5 , 21 5

Correct answer

C. 72 5 , - 21 5

Step-by-step solution

Given, The system of equations x + 2 y + 3 z = 3   . . . . . . 1 4 x + 3 y - 4 z = 4   . . . . . . . . . 2 8 x + 4 y - λ z = 9 + μ   . . . . . 3 Now using the operation, equation 1 × 4 - 2 we get, 5 y + 16 z = 8   . . . . . . . . 4 Now using the operation, equation 2 × 2 - 3 we get, 2 y + λ - 8 z = - 1 - μ   . . . . . . . . 5 Now using the operation, equation 4 × 2 - 3 × 5 we get, 72 - 5 λ z = 21 + 5 μ Now given system of equation has infini

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