Solving Node Voltages for V1 & V2

[stau40]

Homework Statement

The problem asks to find the node voltage for V1 and V2.

Homework Equations

(V1/40) + ((V1-V2)/8) - 6 = 0
((V2-V1)/8) + 1 + (V2/120) + (V2/80) = 0

The Attempt at a Solution

I have simplified the above equations to:
(6V1/40) - (V2/8) = 6
(35V2/240) - (V1/8) = -1

How can I solve from this point? I have read to use Cramers method, but I'm not sure how to apply this. I have plugged in many numbers without any luck, but there has to be an easier way then just guessing?

Thanks in advance!

 

[cepheid]

Without seeing the circuit, there's no way we can check your work.

However, if I ASSUME that your equations are correct, then I should point out that you have only two unknowns, and two equations, which means that you can come up with an exact solution. All you have to do is use one of the equations to solve for one of the unknowns (e.g. V1) in terms of the other. Then substitute this expression for V1 into the second equation (effectively eliminating that variable). Solve for V2. You're done.

EDIT: Yeah, you could use Cramer's rule here too, but it seems like overkill. It's a good way to check your work.

http://en.wikipedia.org/wiki/Cramer's_rule