To clarify something in the video:
The second method I use is useful here because by subtracting the two equations, one of the variables goes away, namely y in this case. In order for this to work all the time we may need to multiply each equation by some number in order to get the cancellation we want. Personally I find this more tedious, and I simply use the first method all the time since it always works. In the problem given, the second method happened to be slightly faster.