let y = A Chorus Line; and x = Beauty and the Beast.
x = y - 676 (1)
x + y = 11598 (2)
We can solve the system by equaling both equations, as follows:
x = y - 676 (1)
x = 11598 - y (2)
y - 676 = 11598 - y
2y = 11598 + 676
2y = 12274
y = 6137 performances of A Chorus Line.
Now we substitute the y value on any of both equations:
x = 6137 - 676
x = 5461 performances of Beauty and The Beast