The first equation is incorrect; it should be:Mesh analysis, final answer.
Make 4 current loops clockwise. I1 is where marked, then continuing around to the right then up for I2 (thru 24 ohm), I3 (thru 4 ohm) and I4 (thru 20 ohm).
By inspection:
I1 - I3 = 3A
-I2*24 + (I3-I2)*15 = 100V
I3 - I4 = 3*I1
6*I1 + 24*I2 + 4*I3 + 20*I4 = 0
That's 4 equations in 4 unknowns.
The first equation is incorrect; it should be:
I4 - I1 = 3A
totally agreedWhile I trust he checked the other equations as thoroughly, it's not *my* assignment, and the ultimate answers calculated should be verified.