Yes, the question states for the given figure, find the current in all resistors

Question

Yes, the question states for the given figure, find the current in all resistors and the voltage with respect to ground at their common node using two methods: a.) Current: Define branch currents I1 and I2 in R1 and R2, respectively; identify two equations and solve them. B.) Voltage: define the node voltage V at the common node; identify a single equation; and solve it. Which methods is preferred. Thanks for the help.

Explanation / Answer

I2+I1= I3 (10-v)/5k+(15-v)/10k = v/2k => (20-2v)/10k+(15-v)/10k= v/2k => 40-4v+30-2v= 10v => 70=10v+4v+2v =>16v=70 =>v=4.375 V I1=(15-v)/10k = I2=(10-v)/5k= I3=v/2k= plugin v get the answer

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