It may be interesting to note that the Y(R-Y)(B-Y) was originally developed for backward compatibility with black-and-white television.
Originally, TV stations only transmitted the black and white signal (which is somewhat of a misnomer since it was an analog signal that could, and still can and does, transmit any level of gray from black to white, not just black and white).
When the time was ripe for color TV while most people still only owned a black-and-white set, it became clear that transmitting an RGB signal separately from a black-and-white signal would be highly impractical.
Instead, a system was needed in which a TV station could transmit a signal that could be seen as monochrome on the older but still common black-and-white TV sets, but the same signal should be in color on the new color TV sets.
That meant, first of all, that the signal had to continue to have the black-and-white image, and the color information had to be added to it transparently.
The black-and-white signal is simply the luminosity of the color and can be calculated by a formula of this type:
Y = a * red + b * green + c * blue
In that formula, a, b, and c are constants (their value depends, among other things, on the type of phosphors used in the TV monitors of that era).
Because of that, it is possible to transmit any RGB color as luminosity, plus any two of the three color channels, then recalculate (with an analog circuit) the third color channel.
Furthermore, all of the new signal had to fit within a limited bandwidth as apportioned during the black-and-white days. Hence, the transmital of the difference of the two channels from luminosity.
This turned out to be quite an advantage the original designers of the system probably did not even realize: Many special effects were created by manipulating the value of the "chroma" (i.e., the R-Y and B-Y) while leaving the luminosity (the Y) unchanged. Other effects are possible by manipulating the Y signal while leaving the other two unchanged. And, of course, the chroma key (a.k.a. the blue screen as well as the green screen) is possible because of the separation of the signal into luminosity and chroma.
Nowadays, just about all of these effects are done digitally, even in software, such as Photoshop, for images that have nothing to do with television.
But who knows, we might not have them all today had it not been for the original problem of making color TV backward compatible with the old black-and-white TV. | 
