The question is: Solve for ia, ib, and ic using two supermesh equations.

I am having a bit of difficulty with this question, as I don't know how to handle the two current sources that are both in loop a.
I tried a few different approaches, such as ignoring both current sources (which didn't get me anywhere, and creating a supermesh between loops a and b, then another between a and c. During this process, I ran into the issue of dealing with the current source that was not removed to create the supermesh.
After this issue is resolved, the rest should be easy.

Any help is appreciated.

 

Another approach is to simplify the circuit as in the attachment.

 

t n k,

Is IS2 oriented in the proper direction on your circuit reduction?

 

t n k,

Is IS2 oriented in the proper direction on your circuit reduction?

Based on the OP's diagram - yes it is.
Current Is2 flows into the left hand node formed with the Is2 current source and R1 & R2.

 

The question is: Solve for ia, ib, and ic using two supermesh equations.

I am having a bit of difficulty with this question, as I don't know how to handle the two current sources that are both in loop a.
I tried a few different approaches, such as ignoring both current sources (which didn't get me anywhere, and creating a supermesh between loops a and b, then another between a and c. During this process, I ran into the issue of dealing with the current source that was not removed to create the supermesh.
After this issue is resolved, the rest should be easy.

Any help is appreciated.

I think you will have only 1 supermesh equation, and two constraint equations. Show some of your work.