Basic circuit analysis question

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Help you to solve, of course:

You need to equations with two unknown. Put the two equations together and calculate the unknown.
 

Replace the Black Box by a Thevenin circuit, is valid because it has only resistors and independent sources, then write the equations:

Vth - Rth 9 = 9
Vth - Rth 6 = 24​

- Find Vth,Rth
- Then Icc = Vth/Rth
 
or intuitively the change in voltage and current at the black box reflects effective series resistance of the black box and Voc and Isc is easy to calculate .

so 9V@9A and 24V@6A has a difference , deltaV/deltaI = 15V@3A or 15/3=5Ω so you can now calc the Voc and Isc directly for Ohm's law. ( but above is more direct math approach)

so 1st case 9A would drop 9*5 = 45V inside black box + 9V = 54V =>Voc
and Isc= 54V/5Ω = 10.8A

of course 1st case is obviously a 1Ω R outside (9V@9A) and inside above we figured out Rin=5Ω so total is 6Ω and 54V/6Ω= 9A which was given.
and 2nd case is obviously 4Ω so 5+4Ω=9Ω form 54V would **** 54/9 = 6A which agrees also.
so that is a confirmation. calculations are correct.
 
excuse me, is this off an online test? i would like to do it, so if possible please post the details.
thanks in advance
 

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