Question

Circuit analysis - my answers seem to deviate from those given.

Answer 1

The answers are
i1=1.180A,i2=-1.240A,i3=-0.058A,i4=-0.529A, and i5=0.471A.

Answer 2

I setup a system of linear equations using mesh analysis, for i1,i3,and i5, renaming them respectively as i_a,i_b,and i_c.
the system I came up with is
6i_a+4(i_a-i_b)=12
2(i_b-i_c)+4(i_b-i_a)=6
2(i_c-i_b)+2i_c=2

or

10i_a-4i_b=12
-2i_a+6i_b-2i_c=6
-2i_b+4i_c=2

but this comes out to i_a=44/21, i_b=47/21, and i_c=34/21