SOLUTION: You invested $17,000 in two accounts paying 4% and 9% annual interest, respectively. If the total interest earned for the year was $1380, how much was invested at each rate?

Let x and y be amounts invested at 4% and 9%, respectively.


Then you have this system of equations

     x +      y = 17000,      (1)    (for total)
0.04*x + 0.09*y = 1380.       (2)    (for the amount earned)


By solving these equations, you can determine the unknown values x and y.


As a first step you can multiply eqn(1) bu 100 (both sides) to get

     x +      y =  17000,     (1)    (for total)
   4*x +    9*y = 138000.     (2)    (for the amount earned)


Next, you can express  one of the two unknowns from the eqn(1) and substitute to eqn(2). In this way you will get a single equation 
for one unknown, which you can easily solve.
It is how the Substitution method works.