Explanation:
Note: Refer the diagram attached
Apply KVL around [tex]i_{z}[/tex] loop
[tex]\begin{aligned}&5 k \left(i_{z}-i_{y}\right)+2 v_{\Delta}=0\\&5000\left(i_{z}-i_{y}\right)+2 v_{\Delta}=0 \quad \ldots \ldots(1)\end{aligned}[/tex]
[tex]From the circuit, \(v_{\Delta}\) can be expressed using ohm's law as,\\\(v_{\Delta}=(1 k ) i_{y}\)\(v_{\Delta}=1000 i_{y}\)[/tex]