How much was invested at each rate?

Question

You invested $4000 between two accounts paying 5% and 7% annual interest, respectively. If the total interest earned for he year was $260, how much was invested at each 

Answer 1

Let X be the amount invested at 5% and Y be the amount invested at 7%.  The system that represents the problem is:

X + Y = 4000

.05X + .07Y = 260  -->  5X + 7Y - 26000

Solving by elimination (subtract 5 times the first equation from the second)

2Y = 6000  -->  Y = $3000

X = 4000 - 3000 = $1000