Discussion Forum



1)

Let  $a,\lambda,\mu \epsilon R$ . Consider the system of linear equation ax+2y=λ and 3x-2y= μ . 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 $\mu$

B) $a\neq-3$, then the system has a unique solution for all values $\lambda $ and $\mu$

C) If $\lambda+\mu=0$, then the system has infinitely many solutions for a=-3

D) If $\lambda+\mu\neq0$ then the system has no solution a=-3

Answer:

Option B,C,D

Explanation:

Here, ax+2y=λ

and 3x-2y=μ

For a=-3 , above equations will be parallel  or coincident, ie, parallel for $\lambda+\mu\neq0$ and coincident. If $\lambda+\mu=0$ and if a≠ -3, equations are intersecting , i.e, unique solution