ac = r ... (1)
ad = s ... (2)
bc = t ... (3)
bd = u ... (4)
(1) => c = r/a
Sub into (3), b(r/a) = t => b = at/r ... (5)
(2) => d = s/a
Sub into (4), b(s/a) = u => b = au/s ... (6)
(5) = (6) => at/r = au/s
st = ru
If st = ru the solution is b = at/r or au/s and c = r/a and d = s/a
If st <> ru, the equations become inconsistent and there is no solution