I spent a few lessons teaching S.E. i started by giving them the following
x + y = 10
What could x and y equal?
students spent time thinking of responses. Eventually students came to the conclusion it had an infinite amount of solutions. I then introduced a different equation:
x – y = 4
Again, eventually they realised there was an infinite amount of solutions. I then asked if any solutions fit both equations.
After a few lessons on SE i realised the common errors were cropping up:
Not always eliminating correctly when solving for one variable
If multiplying an equation through, forgetting to multiply every term
Finding solutions that worked for only one equation.
I created a document to get students to spot the common errors and decide on what the best advice would be:
This worked well and students seemed to recogise these errors in their own work
A few lessons later i gave them a task to unscramble 3 SE questions that had been mixed. I left the original questions up and said they could work through the questions alone and then check using the sheet to see if they were right or the could cut and rearrange the answers. This worked well to support the students who were struggling with the topic
I have made a slide with some questions that might be discussed before you try formal SE questions