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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

$\mu$

$a\neq-3$ , 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

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Answer:

Explanation: