Guys l would like to know how does the the voltage at node D become :
Calculate ix = (VC-VA)/2. You see why this is, I hope. Ask if you don't.
Then the dependent source feeding VD has a voltage VD =-2*ix. Substituting what we calculated for ix above, we have VD = -2*ix = -2*(VC-VA)/2 = VA-VC.
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