I'll be teaching a U.S. college, freshman-level, pre-proofs discrete math course (for future teachers) this semester and one of the topics I like to cover is determining if a system of (usually linear) Diophantine equations has a solution via modular reasoning.
For example: Consider the system: $$3x+5y=7$$ $$9x-7y=12$$ A quick consideration modulo 2 (or thinking about odds and evens) shows that this does not have solutions. Some examples I use in class require other moduli.
The problem I have is that I cannot find a good exposition (print, video, or web) of this topic at the students' level. Everything I find is mired in a more advanced exposition on linear Diophantine equations suitable for a proof-based Number Theory course.
Does anyone else cover this type of reasoning with this level of student? Do you know of any (print, video, or web) materials that might be helpful to share with my students?