Answer:
Va = -2.556 V
Vb = 4.030 V
Explanation:
The two node voltages can be designated Va and Vb for the left and right nodes, respectively. KCL tells you the total of currents out of the node is zero. We can use this fact to write two equations for the node voltages.
6 +(Va -Vb)(1/2 +1/3) +Va/5 = 0
-7 +(Vb -Va)(1/3 +1/2) +Vb(1/8 +1/4) = 0
We can multiply the first equation by 30 and the second equation by 24 to clear fractions. Then the augmented matrix for the node voltages is ...
[tex]\left[\begin{array}{cc|c}31&-25&-180\\-20&29&168\end{array}\right][/tex]
The solutions are ...
Va = -340/133 ≈ -2.556
Vb = 536/133 ≈ 4.030
_____
Additional comment
The magnitudes of the currents in the resistors are ...
Ohms: amps
2: 3.293
3: 2.195
4: 1.008
5: 0.511
8: 0.504
