FIND THE EQUIVALENT RESISTANCE BETWEEN A AND B? (INSTANT 10 POINTS) (DIAGRAM SHOWN)

http://www.flickr.com/photos/76451574@N0…

PLEASE WRITE ALL THE STEPS/WORKING.

ANSWER IS 7 ohm.

Refer to the figure below.
http://www.flickr.com/photos/52771834@N0…

Let x, y and z be the currents through R1, R2 and R3 in the directions shown.
x - z is the current through R4 and y + z is the current through R5 in the directions shown.

Applying Kirchhoff's second law to the upper loop,
5(x + z ) = 10y
=> x + z = 2y ... ( 1 )

Applying Kirchhoff's second law to the lower loop,
5(z + y + z) = 10 (x - z)
=> 2x - 4z = 2y ... ( 2 )

Eliminating y from ( 1 ) and ( 2 ),
x - 3z = 0
=> x = 3z

From eqn. ( 1 ),
y = (1/2) (x + z) = 2z

=> Va - Vb
= 5*(3z) + 10*(2z)
= 35z ... ( 3 )

Main current = x + y = 3z + 2z = 5z
If Re = equivalent resistance,
Va - Vb
= Re * 5z ... ( 4 )

From ( 3 ) and ( 4 ),
Re = 7 ohm.

Edit:
Figure posted.

You are right about the error. I have been making errors of late which I think is due to aging. Several of my contacts have drawn my attention to my making errors, but I keep doing them despite taking care.

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the problem can also be solved by using delta - star conversion

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Yes, vinay, I had forgotten about it. I had learn it as a part of electrical engineering syllabus in college, but as a tutor of 12th std., I was not allowed to use. So, it did not occur. delta-star conversion is a better method. I shall refresh it and post the solution here.

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For star-delta conversion, Refer to fig. http://www.flickr.com/photos/5…