Since you didn't show your steps in solving, there's no way to know where you might have "done wrong". Sorry!
Thank you for showing your set-up. Your equations look fine to me. To solve, let's try substitution:
. . . . .L - S = 9
. . . . .L = S + 9
. . . . .4(S + 9) = 10S
. . . . .4S + 36 = 10S
. . . . .36 = 6S
. . . . .6 = S
Then what must L equal?
Note that you can check your answer to any "solving" problem by plugging it back into the original exercise. If the larger number were, as you propose, equal to 90, then the smaller number will be 90 - S = 6, or S = 84. But 4(90) = 360, and 10(84) = 840.