SATHEE: Straight Line and Pair of Straight Lines 1 Question 41

Straight Line and Pair of Straight Lines 1 Question 41

41. Let $a, λ, μ \in R$ . Consider the system of linear equations $a x + 2 y = λ$ and $3 x - 2 y = μ$ .

Which of the following statement(s) is/are correct?

(2016 Adv.)

(a) If $a = - 3$ , then the system has infinitely many solutions for all values of $λ$ and $μ$

(b) If $a \neq - 3$ , then the system has a unique solution for all values of $λ$ and $μ$

(d) If $λ + μ \neq 0$ , then the system has no solution for $a = - 3$

Show Answer

Solution:

Here, $a x + 2 y = λ$

and $3 x - 2 y = μ$

For $a = - 3$ , above equations will be parallel or coincident, i.e. parallel for $λ + μ \neq 0$ and coincident, if $λ + μ = 0$ and if $a \neq - 3$ , equations are intersecting, i.e. unique solution.

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Straight Line and Pair of Straight Lines 1 Question 41

41. Let a,λ,μ∈R. Consider the system of linear equations ax+2y=λ and 3x−2y=μ.

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41. Let $a, λ, μ \in R$ . Consider the system of linear equations $a x + 2 y = λ$ and $3 x - 2 y = μ$ .