In the lesson linked below, students will explore all three methods of solving a system of linear equations by working collaboratively to solve the same problem by substitution, elimination and graphing. When solving the problems, students will learn that for some systems, some methods may be more appropriate than others and identify their favorite method of solving. Students will create a thinking map in which they will list all three methods and write a sample problem that would be easiest to solve using that particular method.
Lesson guidelines: http://auhsdmath.pbworks.com/w/file/fetch/60768950/6_0Teach_Dir_SystemsB%281%29.pdf
Putting it together: http://auhsdmath.pbworks.com/w/file/fetch/60768951/6_1_Putting_It_Together%281%29.pdf
Systems thinking map: http://auhsdmath.pbworks.com/w/file/fetch/60768952/6_2_Systems_Thinking_Map%281%29.pdf