Question 2371
First define...

Let x = amount invested at 6% rate
Let y = amount invested at 9% rate

so, after 1 year, 0.06x + 0.09y = 684 --eqn1

Also, we know that x+y=10000 --eqn2

Eqn2 is re-written as x=10000-y, and then sub this into eqn1, to give 

0.06(10000-y) + 0.09y = 684
600 - 0.06y + 0.09y = 684
0.03y = 84
y = 2,800

so, x= 7200

jon.