I found it easier to multiply both sides by 600 and simplify before distributing. I get the an equivalent answer and less fractions to deal with. V1=(60+5V2)/11
Solving 2 equations comes handy using crammers rule, it's almost impossible to miss something out in it. But what aches my head is 3 or more equations on those nodal analysis equations, I hate them, first I have to sum up all the common voltage fractions into one fraction and then putting the equations into a matrix to solve it, i almost always miss something in the first trial.
Unfortunately, that is a big weakness for me as well so I don't really have any thoughts or advice on it. The "just be careful and thorough" adage that I keep telling myself is important but not really that useful. Hopefully someone else chimes in, I'd love to get some help with this as well.
Thanks for all your comments! For this one, I skimmed over the setup equations for time. But, if you're not familiar with what happened on that portion, it's probably best to review some of our Circuits 101 videos, particularly the Kirchhoff's videos. Once you understand the circuit analysis portion, then it's not that big of a jump to using them with matrices.