This is a keynote presentation (PowerPoint for Mac). I use these presentations every day to teach from. Instead of spending all my time writing the problem on the board allow the slideshow to do all the work for you. Using the slideshow will allow you to focus on students instead of writing the problem down. You can edit all of the slides if you want to tailor the lesson to your needs.
The presentation is set up to first explain the process then allowing students plenty of opportunity to practice. I usually set it up so that when the problem is presented, students work on it while I walk around the room to check for understanding. The worked out solution is provided for each problem to allow students to identify their errors. You simply click once to present the problem for student to work on, then click a second time to display the worked out solution to the problem.
This presentation includes how to solve systems of equations with three different variables. I also have presentation on solving systems with two variables and real life scenarios.