00:01
The topic of this question is systems of linear equations.
00:06
This question gives us a system of three linear equations, which can represent three unknown currents in a circuit, and these equations represent relationships that can be derived using kirchhoff's current rule, or k -c -l, which is his law.
00:31
So we want to solve for these three currents, i1, i2, and i3.
00:37
You can do that using elimination or substitution.
00:44
So notice that we have i1 pretty much isolated here, and so we can use that to substitute into this equation, the other equation with i1.
00:56
And then that will give us that i3 equals something in terms of only i2, because i1 will be eliminated.
01:08
And then using that expression of i2, we can substitute this i3 into the third equation, which would leave us with one equation with just i2 in it.
01:22
So let's do that.
01:27
Notice here we have a common factor of 2, so we can just divide both sides by 2.
01:39
In fact, the same thing can be done here.
01:45
And so we can substitute this i1 into here once we divide by 4 as well.
01:54
And so this substitution gives us that i3 equals 1⁄2 plus 7 over 4 i2...