AC steady state circuit analysis using mesh
first you talk about a linear system of 3 equations but you don`t show your starting equation so it is really hard to nail down what error you made.

However, I offer an alternative to resolve this problem. Because it is a linear circuit and you only have 2 sources, you can use the superposition principle.

http://www.allaboutcircuits.com/textbook/direct-current/chpt-10/superposition-theorem/

In most cases, it is easier to resolve , but the trade offs is that the problem will take more time to be resolve.

Regards, MathieuL