00:01
Okay, so we're given the system of linear equations, a -x plus b -y equals 1, and b -x plus a -y equals 1.
00:06
And we want to find x and y in terms of a and b.
00:10
So first we'll go ahead and do a substitution.
00:13
We'll find our substitution term, which we're going to use this top one over here, which will end up giving us x equals 1 minus b -y with 1 over a.
00:33
And we'll be going ahead and substituting it into there, which will give us b times 1 over a, 1 minus by plus ay equals 1.
00:57
And so then once we've done that, we can get b over a minus b squared over a y plus ay equals 1.
01:16
And we'll go ahead and times the whole thing by a.
01:19
That way we'll end up getting b minus b squared y plus a squared y equals one so then when we go ahead and get separate y we'll get y we'll get y times a squared minus b squared equals one minus b so then to finish this out we will get y equals one minus b over a squared minus b squared.
02:02
And we know we can divide by a squared minus b squared because we have a squared minus b squared does not equal zero.
02:07
So then that is valid.
02:09
And so now that we've got that, we're going to do back substitution into x back sub, which we're going to go back over here because this part of the board is actually clear while the other side is most certainly not...