Q1 / 124 · NTA Abhyas (JEE Main) 2020 · Mathematics · Determinants

Let a,λ,μ∈R. Consider the system of linear equations ax+2y=λ and 3x-2y=μ. Which of the following statement is INCORRECT?

  • Correct answer
    A
    If a=-3, then the system has infinitely many solutions for all values of λ and μ
  • B
    If a≠-3, then the system has a unique solution for all values of λ and μ
  • C
    If λ+μ=0, then the system has infinitely many solutions for a=-3
  • D
    If λ+μ≠0, then the system has no solution for a=-3

Solution

ax+2y=λ
3x-2y=μ
For a=-3, above lines will be parallel or coincident
Also parallel for λ+μ≠0 and coincident λ+μ=0
and if a≠-3, lines are intersecting ⇒ unique solution.

Hence, the correct answer is option: 'A'.

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