How Does Substitution Work in Mesh Analysis Equations?

[Novark]

I understand everything up to the point which I've marked in red...

Can anyone explain those few lines?

I would greatly appreciate it!

Thanks.

 

[muhandis]

Seems like KCL (Kirchoff's Current Law) at node A.
i1 = i0 + i2

(sum of currents entering) = (sum of currents leaving)

 

[Novark]

Seems like KCL (Kirchoff's Current Law) at node A.
i1 = i0 + i2

(sum of currents entering) = (sum of currents leaving)

I understand that part, but how did they derive the equation below that line?

 

[muhandis]

They just substituted into the equation above.

 

[Novark]

They just substituted into the equation above.

Oh, I see it now. I totally misunderstood the fact that they were simply substituting i0 = i1 - i2 into the third mesh equation.

Thanks :-)