Extension - Integers and Algebra - Euchlid's Theory

Read over the article available on the link below. (Values are substituted for the variables that make the expression true.)

                         http://nrich.maths.org/1357


Questions
First we notice that 13x+29y=42 has many solutions, for example x=1, y=1 and x=30, y=−12. Can you find others (it has infinitely many solutions)?

2x+4y=13 has no solutions because 2x+4y must be even and 13 is odd. Can you find another equation that has no solutions?

Post your solutions!!!