0:00
So we have a diagram.
00:02
And let me just kind of draw it here.
00:08
And we know that these are supposed to be, the midpoint is joining.
00:14
So we know that 3x minus 2y is the length of this side from here to here.
00:20
And we know that this one is measured of 8.
00:23
And this is 7.
00:24
And we show that that other quote base is 5x minus 3y.
00:28
And we need to solve for x and for y.
00:31
So again, we know that this is a midpoint.
00:34
So by definition of a midpoint, this segment must be equal to that.
00:38
So we've got one of our equations.
00:39
We know that 3x minus 2y must equal 8.
00:44
There's one equation.
00:46
Now, we also have a theorem that says that if you have a midpoint from each side of a triangle joining them, we would know that this length is cut in half too, but we're not doing anything with this other third side here.
01:00
We know that this segment is half the length of this base.
01:09
So 5x minus 3y must be twice as long as that.
01:16
So it must be 14.
01:19
And now we need to solve this little system...