Circuit analysis with known current
What a lot of people struggle with when it comes to systems of equations is recognizing the easiest equations to make. It is pretty easy to go and make a problem like this overly difficult. It is also easy to start assuming things that are wrong, like you did, and make a mistake.
EDIT: To clarify the mistake you made was not including the voltage of the current source in your KVL equation.
Just to restate the obvious, this problem can be done with 3 equations because you only have 3 unknowns.
Now it comes to deciding which 3 equations to make. Using KVL on the left loop is difficult because there is a current source with no resistor. This means we don't know the voltage there (source transformation) . The right two loops make easy KVL equations because they have no unknown voltages. So how do we make that third equation? Think about KCL for that one.
The only way to get good at these is with practice unfortunately. But what you can do is look for the easiest questions first.