Students will learn to solve linear systems in two variables, using the method of elimination. They'll solve word problems and mathematical ones. Here's an example word problem. Next, give your students this challenge:
How to solve the "working together" riddle that stumps most US college students by MindYourDecisions
This is a work problem, but it requires students to multiply whole equations and add equations together. I believe that adding equations is first encountered when learning to solve systems by elimination.
Next, give your students this challenge, then this one, and finally, this one. Personally, I find Diophantine equations interesting. Here's a set of puzzles that involve Diophantine equations. Here's a solution to the original problem. And here's a related puzzle. Unfortunately, a hint is given, but no solution has been provided.
Conclude by leading this investigation: