Now, since we want to end up with a differential equation in i2,

we have to do algebra to eliminate the i1.

So, we look at which equation has the fewest i1 terms, and we'll use that one.

The second equation here has only one i1 term, so we can solve that for i1.

And then we'll substitute that in to the top equation here.

Now this gets messy and I'm showing you all this for a point.

I want you to see that while this method is very straightforward it can get pretty

pretty messy algebraically.

So now we, I need to make a little room and

we substitute this expression for i1 into the top equation.

And the substitution is wherever you see the square brackets.