Let $a, \lambda , u\mathbb{ }\in \mathbb{R}$ . Consider the system of linear equations
$ax+2y=\lambda$
$3x-2y=\mu$
Which of the following statement(s) is (are) correct ?

• A

  If $a=-3,$ then the system has infinitely many solutions for all values of $\lambda$ and $\mu$
• Correct answer
  B

  If $a \ne -3,$ then the system has a unique solution for all values of $\lambda$ and $\mu$
• Correct answer
  C

  If $\lambda +\mu =0,$ then the system has infinitely many solutions for $a=-3$
• Correct answer
  D

  If $\lambda +\mu \ne 0,$ then the system has no solution for $a=-3$

Hence, the correct answer is options: 'B', 'C', 'D'.