ax + 2y = λ

           3x – 2y = µ

(i)         If $\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$  the infinite solution

           $\therefore \frac{\mathrm{a}}{3}=-1=\frac{\mathrm{\lambda }}{\mathrm{\mu }}$

            ⇒         a = –3 & λ = –µ

            ⇒         λ + µ = 0

(ii)         If $\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}\ne \frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}$  then unique solution

            $\frac{\mathrm{a}}{3}\ne$ –1             ⇒ a $\ne$ –3

(iii)        If $\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}\ne \frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$  then no solution

            a = –3 and λ + µ ¹ 0.

            $\therefore$         no solution

            $\therefore$         BCD. Ans.