The attached guided notes contain half-sheets for your students. There are 4 half sheets, scaling from easy, medium, difficult, and most difficult elimination problems. I have found breaking this concept apart into these four levels of difficult made it easy for my students to grasp elimination.
The guided notes have the students make a plan for each problem, and then execute that plan. I split these four sheets into 4 separate days.
The levels are as follows:
Day 1 - Easy: no need to multiply either equation
Day 2 - Medium: multiply top or bottom equation by a positive number
Day 3 - Difficult: multiply top or bottom equation by a negative number
Day 4 - Most Difficult: multiply top and bottom equation by numbers, sometimes negative and sometimes positive.
All answers are integers. When using this model, my students grasped the concept of elimination quite easily. The ones who didn't had steps and excellent guided notes to look back on. Enjoy!