Current returning to cell A = x
Current returning to cell B = y
Current entering the voltmeter = z
10- 1*x=0
4- 2*y = 0
z = y + x
X=10
Y=2
Z=12
U=RI
1/R=1/1+1/2
1/R=1,5
R=2/3
U = (2/3)*12 = 8
The reading is 8 Volts.
Substitute I3=z, I2=y and I1=x.
System of equations:
z = y + x
12−0.2z−0.02x=0
−10+0.2z+0.1y=0
From second and third equation solve:
x=−10z+600
y=100−2z
Add these to the first:
z=(100−2z)+(−10z+600)
z=700/13
z~53,85
Thus I3~53,85 , I2~-7,7 and I1~61,5
Hope this helps!