Two Variables, One Equation and a lot of headache!

[abemartin87]

If x and y are both non-negative integers, a,b,c are constants.

ax+by=c

has a unique solution, even though we have two unknown variables and one equation.

What if we remove the condition that the values are "integers' but maintain the property that x and y are both non-negative (ie positive or equal to 0).

does ax+by=c still have a unique solution for x and y?


My question I guess boils down to when does this two variable, one equation, that HAS A SOLUTION no longer holds to become two variables, one equation and cannot be determined?


Thank you guys!

[jnelson0612]

abe, question for you--is this example from one of the Strategy Guides? Thanks!