I'm sorry that the figure doesn't look better, it's exactly what was given to us. I'm guessing it's written 3Ix on the independent current source on the right and Ix is the current flowing through 8 Ω on the left mesh. So here are my questions about this figure:

1. Is Ix equal to I1-I2 here?

2. And again, is I3 equal to -3Ix? I really don't understand how independent current sources work. Does that current source determine every current value on that right mesh? How does it work? The currents flowing through left branch of the right mesh are 3Ix, I2 and Ix. I can continue writing some more, but that would be pointless because I'm totally lost there. Please explain how independent current sources work and tell me how to determine the currents on every single branch.

If I can get the answers for two questions above, I believe I can solve for I1, I2 and I3 easily.

So I defined I1 and I2 as it's shown in the figure. My questions about this one:

1. I wrote an equation on green node as the following. I1 + I + 2A = I2.

Is this equation true? Because it looks like a bit wrong. Again, I'm not quite sure about how the independent current source affects the circuit.

If someone can help me fix my troubles on these two, it would be great. I also want to know if these two questions are fundamental ones or challenging ones. Because I seemed to be doing just fine until I saw these.