-E2+I2R2+I3R3=0 ①
-E1+I1R1+I3R3=0 ②
I3=I1+I2 ③
将E1=10V,E2=15V,R1=2Ω,R2=1Ω,R3=5Ω代入得:
-15+I2+I3*5=0 ④
-10+I1*2+I3*5=0 ⑤
I3=I1+I2 ⑥
2④+⑤=I3*15+2*(I1+I2 )-40=0 ⑦
将⑥代入⑦得:I3*15+2*I3-40=I3*17-40=0
解得:I3=40/17
将其分别带入④、⑤得:-15+I2+40/17*5=I2-55/17=0
-10+I1*2+40/17*5=I1*2+30/17=0
分别解得:I2=55/17;I1=( -30/17)/2= -15/17
综上,I1= -15/17;I2=55/17;I3=40/17