Explanation

(c) $- i_{1} + 0 \times i_{xy} + 3i_{2} = 0\ i.e.\ i_{1} = 3i_{2}$ …(i)
Also $- 2\left( i_{1} - i_{xy} \right) + 4\left( i_{2} + i_{xy} \right) = 0$
$i.e.\ 2i_{1} - 4i_{2} = 6i_{xy}$ …(ii)
Also $V_{AB} - 1 \times i_{1} - 2\left( i_{1} - i_{xy} \right) = 0 \Rightarrow 50 = i_{1} + 2\left( i_{1} - i_{xy} \right)$
$= 3i_{1} - 2i_{xy}$ …(iii)
Solving (i), (ii) and (iii), $i_{xy} = 2A$