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Originally Posted by jstark  I don't think I understand how the equations are equal there. |
All three equations represent straight lines. Those lines intersect each other at the points T, U and V.
For example, your equation for TU and your equation for UV intersect at the point U(a,b).
So x = a, and y = b are solutions to BOTH equations, since that point lies on BOTH lines.
If you think of the equations being y = 6x-11 and y = 3x-1. The point at which these two lines intersect lies on both lines. And hence the y-coordinate of that point is equal for both lines.
Hence y = y
Hence 6x-11 = 3x-1
3x = 10
x = 10/3
This is the x-coordinate of the intersection (and hence the x coordinate of point U!). If you plug that value of x into either of the two equations, you'll get the y coordinated for U.