Straight Line and Pair of Straight Lines 1 Question 41
41. Let $a, \lambda, \mu \in R$. Consider the system of linear equations $a x+2 y=\lambda$ and $3 x-2 y=\mu$.
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 $\lambda$ and $\mu$
(b) If $a \neq-3$, then the system has a unique solution for all values of $\lambda$ and $\mu$
(c) If $\lambda+\mu=0$, then the system has infinitely many solutions for $a=-3$
(d) If $\lambda+\mu \neq 0$, then the system has no solution for $a=-3$
Show Answer
Solution:
- Here, $a x+2 y=\lambda$
and $3 x-2 y=\mu$
For $a=-3$, above equations will be parallel or coincident, i.e. parallel for $\lambda+\mu \neq 0$ and coincident, if $\lambda+\mu=0$ and if $a \neq-3$, equations are intersecting, i.e. unique solution.
