Sounds like a dual equation, but I am having difficulty

Question

Joe has a collection of nickels and dimes worth $7.10. If the number of dimes were doubled and the number of nickels increased by 10, the value of the coins would be $13.40. How many dimes does he have?

Answer 1

nickels = N nickels are worth 5 cents

dimes = D dimes are worth 10 cents

Thus, 

5N + 10D = 710

 

If the dimes are doubled, we have 2D dimes

If the nickels are increased by 10, we have N+10 nickels.

Then, 

5(N+10) + 10(2D) = 1340

5N + 50 + 20D = 1340

5N + 20D = 1290

We have 2 equations

5N + 10D = 710

5N + 20D = 1290

Subtract the top equation from the bottom

10D = 580

D = 58

5N + 10D = 710; substituting D = 58

5N + 10(58) = 710

5N + 580 = 710

5N = 130

N = 26