Solve the system Ax + y = B, x + By = A for x and y.
Ax + y = B ---> y = B - Ax
x + By = A ---> x + B(B - Ax) = A (substitute)
x + B2 - ABx = A (distribute)
x - ABx = A - B2 (subtract)
x(1 - AB) = A - B2 (factor)
x = (A - B2 / (1 - AB) (divide)