Determine the currents I 1 , I 2 , and I 3 in the figure above. Assume R = 20 ?

Question

Determine the currents I1, I2, and I3 in the figure above. Assume R = 20 ? and the internal resistance of each battery is r = 1.0 ?.

I understnad that I have to use Kirchoff's rule, and am able to solve for the following values correctly:

I1 = 0.77

I2 = 0.71

I can't seem to get the answer for I3 however. I thought that because I1 = I2 + I3, I3 should equal 0.06, but it doesn't.
Also, how do I use R = 20? I sort of ignored it for the first part, so im sure that that is why im getting I3 wrong. Any help would be really appreciated! Thanks!  

Determine the currents I1, I2, and I3 in the figure above. Assume R = 20 ? and the internal resistance of each battery is r = 1.0 ?.

Explanation / Answer

assuming Ix AND Iy as mesh currents in clockwise directions

Ix+12+12*Ix+11*(Ix-Iy)+12+8*Ix=0

32Ix-11Iy=-24 ----(i)

-12+11*(Iy-Ix)+20*Iy+Iy+6+15*Iy=0

-11*Ix+47Iy=6 ----(ii)

solving the above two equations we get: Ix=-0.767 ,iy=-0.052

I1=-Ix=0.767

I2=(Iy-Ix)=0.715

I3=-Iy=0.052

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