Question 864755
You are right normally we need three equations for three unknowns.
Let's see what we know and how we can use that info
"$24000 is invested in three different accounts
x+y+z=24000,
each paying 1%, 2%, and 3% interest, respectively.
After 1 year, the simple interest earned from all three accounts amounts to $440.
 (.01)x+(.02)y+(.03)z=440 
If the account paying 1% interest contains three times the amount in the account paying 2% interest, 
You forgot this tidbit.

x=3y,
(.01)x+(.02)y+(.03)z=440,
x+y+z=24000
Sometimes you really have to squeeze info to get the three equations. Here you missed a treasure

x=12000.,   y=4000.,   z=8000.