Sue invested $10,000, part at 5.1% annual interest and the balance at 6.3% annual interest. how much is invested at each rate if a 1-year interest payment is $582.72 answer

Let a be the amount at 5.1% and b be the amount at 6.3% interest.
0.051a + 0.063b =582.72 (1)
a + b = 10000
b = 10000 - a (2)

Plugging the expression for b from equation (2) into equation (1), we get:
0.051a + 0.063(10000 - a) = 582.72 (3)
Expanding (3) and collecting like terms, we get:
0.012a = 47.28
a = 3940
b = 10000 - 3940 = 6060
The answer is: $3,940 invested at 5.1% and $6,060 invested at 6.3% interest.

< i think this is the answer unless i did my math wrong