You invest $7200 in two accounts paying 6% and 9% annual interest. at the end of the year, the accounts earn the same interest

Let the final interest = X

If Simple interest is given A=PiN, where A is the final interest, P is the principal, i is the rate of interest and N is the number of terms (years)

∴The first account will be X = H x 0.06 x 1, where H is the principal for that account
And the second account will be X = G x 0.09 x 1, where G is the principal for that account

You can substitute the X value of the first equation (X = P x 0.06 x 1) into the second equation to make: 

H x 0.06 = G x 0.09
∴G = 2/3 x H
∴G/H = 2/3 (makes a ratio of five parts)

Divide 7200 into five parts = $1440 per part

Hence, G = 2 x 1440 = $2880, and H = 3 x 1440 = $4320

0.06x=0.09(7200-x)
0.06x=648-0.09x
0.09x+0.06x=648
0.15x=648
X=648/0.15=4,320 at 6%

7200-4320=2,880 at 9%