Step 1 :Let the amount invested at 5% be x and the amount invested at 2% be y. We have two equations:
Step 2 :1. \(x + y = 19000\) (total investment)
Step 3 :2. \(0.05x + 0.02y = 560\) (total interest)
Step 4 :Solve this system of linear equations to find the values of x and y.
Step 5 :Solution: \(x = 6000\) and \(y = 13000\)
Step 6 :\(\boxed{\text{The amount invested at 5% is }\$ 6000\text{. The amount invested at 2% is }\$ 13000\text{.}}\)