00:02
Okay, for our next problem, we have y equals x cubed minus 3x squared plus 1 and y equals x squared minus 3x plus 1.
00:25
We're trying to find where they intersect and we're going to use the substitution method.
00:29
One nice thing, and i'm going to go ahead and use our second equation for substituting, is that we already haven't solved for y.
00:37
So really we just have to, in the first equation, replace y with the second equation we already have solved for y.
00:48
So we have x cubed minus 3x squared plus 1.
00:55
Then plugging in that bottom equation, we're going to have x squared minus 3x plus 1.
01:05
Okay, so simplifying this down, just moving everything to one side of the equation.
01:09
If we subtract one from both sides, those will cancel out.
01:14
We're going to add 3x, and we're going to subtract x squared.
01:19
So we're going to have 0 equals x cubed minus 4x squared plus 3x.
01:37
Okay.
01:38
Now to go from there, we can factor out an x...