jee-advanced 2016 Q49

jee-advanced · India · paper2 Simultaneous equations
Let $a , \lambda , \mu \in \mathbb { R }$. Consider the system of linear equations
$$\begin{aligned} & a x + 2 y = \lambda \\ & 3 x - 2 y = \mu \end{aligned}$$
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) 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 $a = - 3$
Let $a , \lambda , \mu \in \mathbb { R }$. Consider the system of linear equations

$$\begin{aligned}
& a x + 2 y = \lambda \\
& 3 x - 2 y = \mu
\end{aligned}$$

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) 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 $a = - 3$