Simple Mesh or Node circuit?

Hi everyone.

I received this question as part of a test that I can do in my own time.
Problem is I have not been doing electronics for a long time now so I have allot of catch up work to do.
I have done the problem I would just like peoples opinions on if its correct and if Nodal or Mesh analyses would have been a better quicker option.
I used Mesh



A: 48=4(ia-ib)+8(ia-ic) ; 48 = 4ia - 4ib + 8ia - 8ic ; 12 = 3ia - ib -2ic
B: 0 = 4(ib - i1) + 6ib + 2(ib - ic) = 0=4ib - 4ia + 6ub + 2ib -2ic ; 0 = -4ia +12ib -2ic ; 0 = -2ia + 6ib - ic
C: 0 = 2(ic -ib) +8( ic - ia) ; 0 = -4ia -ib + 5ic

So when plugged into a Matrix and get the inverse I get the following

| 29 7 13| |12|
1/21| 14 7 7 | | 0 |
| 26 7 7 | | 0 |

So multiplying it out I get

ia = 16.57A
ib = 8A
ic = 14.857A

Finding I.
I = ia = 16.57A

Finding I1.
I1 = ( ia - ic ) = ( 16.57 - 14.857 ) = 1.713A

Does this seem correct?
Thanks

It's OK

But you could avoid a 3x3 system by separating the R_6ohm because does not affect the others.



Also you could write node equations -> only one unknown V(1/4+1/8+1/2) = 48/4 ==> V = 96/7 ≈ 13.71428571

Then I = 48/6 + (48-V)/4 = 116/7 ≈ 16.57142857

and I1 = V/8 = 12/7 ≈ 1.714285714