Algebra 2 help? Its a word problem

Ok so i hav this hw nd i hav no idea how to do this. Please show me the steps nd everything. Thank you!

Here is the problem...

A man invested $6000, part of it at 5% simple interest and the rest at 7% simple interest. If his annual interest income is $372, how much did he invest at each rate?

Let a = amt inv @ 5% and b = amt inv @7%

a + b = 6000
0.05a + 0.07b = 372

a = 2400, b = 3600

He invested $2400 at 5% and $3600 at 7%.

-0.05a - 0.05b = -300

0.02b = 72
b = 3600
a = 2400

x+y=6000

.05x+.07y=372

x=2400
y=3600