In one year, Michael earned $6300 as a work study in college. He invested part of the money at 9% and the rest at 7%. If he received a total of $493 in interest at the end of the year, how much was invested at 7%? How much was invested 9%?

Let x represent invested money at 9% and y at 7%

Now we write system:

x+y = 6300

1.09*x + 1.07 * y = 6300 + 493 = 6793

1.09x + 1.09y = 6867

Here we multiplied first equation with 1.09 and now we will subtract second from first:

0.02y = 74

y = 3700

x = 6300-3700 = 2600

Michael invested 2600 at 9% and 3700 at 7%