After moving onto some of the practice textbook exercises in the section covering Kirchhoff's current law and Ohm's law, I came across a problem which evades my best attempts at solving it.
Using Ohm's law, it was relatively easy to determine a equation involving voltage drops around the right loop:$$(1000\,\Omega)I_C+(1000\,\Omega)I_E=V_2\\(1000\,\Omega)(I_C+I_E)=V_2$$Similarly, it was simple to write an equation for the node where $I_B,I_E$ meet:$$I_B+I_C+150I_B=I_E\\151I_B+I_C=I_E$$... but given just $I_B=100\,\mu A=10^{-4}\,A$ it seems impossible to determine a numerical value for $I_C,I_E$.
Nevertheless it's straightforward to solve for $I_C,I_E$ in terms of $I_B,V_2$:$$I_C+I_E=\frac1{1000}V_2\\-I_C+I_E=151I_B\\\implies\begin{align*}2I_E&=151I_B+\frac1{1000}V_2\\2I_C&=-151I_B+\frac1{1000}V_2\end{align*}$$
Substituting $I_B=10^{-4}\,A$ yields $I_C=\frac1{20000}(10V_2-151),I_E=\frac1{20000}(10V_2+151)$
Am I approaching the problem correctly? Am I justified in ignoring the unlabeled voltage source bridging the two loops along with the labelled elements in the left one (i.e. $V_1,R_1,R_2$)? Am I treating the CCCS properly in writing my nodal equation?