Solve a circuit with the nodal analysis (1)
I don't think your solution 27.27 V is correct. After correcting your equations, i'm getting:

Current leaving node 1

(V1 - 40)/1 + (V1 - Vo)/2 + 5 = 0
2V1 - 80 + V1 - Vo + 10 = 0
3V1 - Vo = 70  
Vo = 3V1 - 70   ...... (1)


Current entering node 2

(V1 - Vo)/2 + 5 + (-20 - Vo)/8 + (-Vo)/4 = 0
4V1 - 4Vo + 40 - 20 - Vo - 2Vo = 0
4V1 - 7Vo = -20  ..... (2)


Substituting (1) into (2)

4V1 - 7(3V1 - 70) = -20
4V1 - 21V1 + 490 = -20
17V1 = 510
V1 = 30 V


Substituting V1 into (1)

V0 = 3(30) - 70 = 20 V