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JEE Main202226 Jun 2022Morning ShiftMathematicsDeterminantsActual

The ordered pair a , b , for which the system of linear equations 3 x - 2 y + z = b 5 x - 8 y + 9 z = 3 2 x + y + a z = - 1 has no solution, is

Options

  1. A3 , 1 3
  2. B- 3 , 1 3
  3. C- 3 , - 1 3
  4. D3 , - 1 3

Correct answer

C. - 3 , - 1 3

Step-by-step solution

Given system of linear equations are 3 x - 2 y + z = b 5 x - 8 y + 9 z = 3 2 x + y + a z = - 1 For system to have no solution, ∆ = 3 - 2 1 5 - 8 9 2 1 a = 0 ⇒ 3 - 8 a - 9 + 2 5 a - 18 + 1 21 = 0 ⇒ a = - 3 Also, ∆ 2 = 3 - 2 b 5 - 8 3 2 1 - 1 = 3 5 + 2 - 11 + b 21 = 21 b - 7 If b = 1 3 , ∆ 2 = 0 So b must be equal to - 1 3

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