How can I figure out the voltage in this circuit?
Node A: \$ -5 + \dfrac{V_a-V_b}{20} + \dfrac{V_a-V_c}{50} = 0 \$
Node B: \$ -\dfrac{V_a-V_b}{20} + \dfrac{V_b-V_c}{30} = 0 \$
Node C: \$ -\dfrac{V_b-V_c}{30} - 0.01V_1 - \dfrac{V_a-V_c}{50} = 0 \$
\$V_b = 0.4V_1\$

You have four equations but only three unknowns, so you know you have a problem.
Also, your node B equation is incorrect because it doesn't account for current through the VCVS.
I would throw away the node B equation and use the other three.