Row Reduction & Rank · Hard problem

Two batteries, with EMFs $10$ V and $4$ V connected with opposite polarity, drive current through a two-loop circuit sharing a resistor $R$ (ohms), with $6\,\Omega$ and $8\,\Omega$ in the other two branches. Mesh analysis gives $(6+R)i_1-Ri_2=10$ and $-Ri_1+(8+R)i_2=-4$. Find the value of $R$ for which $i_2=0$ (no current flows in the second loop, a balance condition used to measure $R$).