A more readable (and scalable?) version of these equations can be formulated as a linear system:

[x]    [x_A]    [x_B]    [x_C]
[y] = a[y_A] + b[y_B] + c[y_C]
[1]    [  1]    [  1]    [  1]

or, to directly calculate:

[a]   [x_A  x_B  x_C]-1 [x]
[b] = [y_A  y_B  y_C] * [y]
[c]   [  1    1    1]   [1]

Thanks for the matrix-vector form of these equations, they were really helpful! Do you know if clockwise or counter-clockwise directionality affects these equations?

For these equations clockwise vs counter-clockwise doesn't matter, you just have to make sure that the orderings of all the variables are consistent with each other (e.g. a,b,c; x_A,x_B,x_C; y_A,y_B,y_C)