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JEE Advanced2016MathematicsDeterminantsActual

Let a , λ , u ∈ R . Consider the system of linear equations a x + 2 y = λ 3 x - 2 y = μ Which of the following statement(s) is (are) correct ?

Options

  1. AIf a = - 3 , then the system has infinitely many solutions for all values of λ and μ
  2. BIf a ≠ - 3 , then the system has a unique solution for all values of λ and μ
  3. CIf λ + μ = 0 , then the system has infinitely many solutions for a = - 3
  4. DIf λ + μ ≠ 0 , then the system has no solution for a = - 3

Correct answer

B. If a ≠ - 3 , then the system has a unique solution for all values of λ and μ

Step-by-step solution

a x + 2 y = λ 3 x - 2 y = μ If a = - 3 lines will be parallel or coincident, parallel for λ + μ ≠ 0 and coincident if λ + μ = 0 and if a ≠ - 3 lines are intersecting ⇒ unique solution. If parallel then no solution & If coincident then infinite solution

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