Data Sufficiency

Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?

1) She bought $4.40 worth of stamps.

I rephrased this question to

15x + 29y = 440.

I understand how to get the solution of x=10, y=10. My question is how do I recognize that 15x+29y = 440 has 1 solution(x=10,y=10). When I first saw this problem I assumed that since I didn't have another equation in terms of x and y I couldn't solve for x and y since I didn't have 2 equations for 2 unknowns. I am just wondering if I see this on the GMAT then how I would recognize to go ahead with trying to find 1 solution.

Thanks.

from one equation with two variables (x and y), you cannot reliably find out both their values. you need to translate x or y, so that we have only one variable. if we knew there were 20 stamps bought, then we could place y = 20-x in the equation. So statement 1 is not sufficient. the answer should be C or E