Hello. May somebody please explain to me why creating a clockwise or countercloc

Question

Hello. May somebody please explain to me why creating a clockwise or counterclockwise Kirchoff loop from acfe does not give me the correct answer. I looked at the solution below from chegg and I want to know why I do not get the same values for the current.

I made a loop from acfe I got the equation 10V-10i2+15V-10i2=0 which can be simplified as i1=2.5-i2. I then created the same 2nd loop from the chegg answer below which simplified to 1.5V=2i1+3i2. I then substituted my equation 1(I plugged in i1=2.5-i2) into equation 2. I then solved and got i2=-3.5. I then reversed the direction of the Kirchhoff loop in the counterclockwise direction and I got the same answer since the reverse direction was multiplying the first equation by (-1).

Explanation / Answer

its not big mistake done by you. 15 V battery is dominating the 10 V battery but you took the direction of i2 in down ward direction but due to high voltage battery the current i2 is decided by the higher potential battery thats why you get i2 value as negative, it simply indicates the direction what we choose is reverse than the actual situation.

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