Invariance of solutions when adding equations

When teaching pupils how to solve simultaneous equations by elimination pupils have to add, or subtract equations. This could be something your pupils have never seen before, and the idea that when adding or subtracting equations the solution is unchanged may be quite a leap in conceptual understanding. This prompt attempts to address that.

It could be used when teaching normal linear equations to plant the seeds or just before teaching simultaneous equations once pupils' knowledge of linear equations has matured.

Here are some questions you may wish pupils to consider.

• Solve for x, what do you notice?

• Write two more equations with the same solution, add them together, solve the new equation?

• Will this always be true?

• Does it work for subtraction?

• Does it work for other solutions, when both solutions are the same?

• What about if the solutions are different?

I would love to hear about other lines of inquiry this prompt could take, so any feedback, both constructive and positive, would be great.