Du darfst ruhig mit Brüchen rechnen.
7·x + 12·y = 1000 → y = (1000 - 7·x)/12
200/x = 120/y + 3
200·y = 120·x + 3·x·y
200·(1000 - 7·x)/12 = 120·x + 3·x·(1000 - 7·x)/12
200·(1000 - 7·x) = 12·120·x + 3·x·(1000 - 7·x)
200000 - 1400·x = 1440·x + 3000·x - 21·x^2
21·x^2 - 5840·x + 200000 = 0
x = 5000/21 ∨ x = 40