[kelicker]

Thank you for your response. This is helpful. May I ask, are we interpreting this standard correctly? It is not talking about proving why we can use the Elimination method to solve for a variable, right? Instead it is talking more about why elementary row operations preserve the solution set? Everyone that I have talked to was interpreting this standard as referring to the Elimination method (including, it seems, the Progressions).

[kelicker]

I am still having the same trouble as nvitale. The proof that has been described by the progressions is of simply adding (or subtracting) the two equations together. This produces one new equation that is true. This standard seems to be talking more about the row operations of matrices where you “replace one equation by the sum of that equation and a multiple of the other.” This results in a system of equations where one equation is the same as one of the original equations and the other equation is a new hybrid of the first two original equations. It is asking why this new system has the same solutions as the original.

I do not think this standard is addressing “The Elimination Method” as we know it where you multiply one or both equations by a constant and add them together. This seems like more of a precursor to performing row operations on a matrix.

I myself do not know how to prove this, and I cannot find any proofs online.

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