Let a ,   λ ,   u   ∈ R . Consider the system of linear equations a x + 2 y =…

Let a, λ, u ∈R . Consider the system of linear equations
ax+2y=λ
3x-2y=μ
Which of the following statement(s) is (are) correct ?
  1. If a=-3, then the system has infinitely many solutions for all values of λ and μ
  2. If a ≠-3, then the system has a unique solution for all values of λ and μ
  3. If λ+μ=0, then the system has infinitely many solutions for a=-3
  4. If λ+μ≠0, then the system has no solution for a=-3

Solution

ax+2y=λ
3x-2y=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

 

Asked in: JEE Advanced 2016 (Paper 2)

Practice more Determinants questions on Aicharya