system of equations

Question

A total of $8000 is split between two accounts with annual interest yields of 6% and 8%. If there was a total of $586 in interest, how much was invested in each?

Answer 1

let x = first account and y = second account

x + y = 8000 ..........................(1)

0.06 x + 0.08 y = 586 ..........................(2)

Now that you have two equations and two unknowns, you can solve by algebraic method. Let's multiply (1) by -0.06 and then add it to (2):

-0.06 x - 0.06 y = -480

0.06 x + 0.08 y = 586

Adding, we obtain:

0.02 y = 106

y = 106/0.02 = 5300

From equation (1), we get:

x = 8000 - y = 8000 - 5300 = 2700

First account: $2700 with 6 % interest

Second account: $5300 with 8 % interest