1. The problem statement, all variables and given/known data Prove that replacing one equation in a system of linear equations by a non-zero multiple of itself does not change the solution of the system. 3. The attempt at a solution I'm still relatively new to proofs, so this is what I have come up with: Let S be a system of n equations and n unknowns and assume that S has a unique solution(is this assumption too strong?). Also assume that the other two elementary operations do not change the solution of S. Let j be an arbitrary row and multiply row j by a non-zero constant k. Now during the elimination process: Let i be the row that includes the current pivot element. Assume i<j, so that the element in the column of the pivot element in row j has to be eliminated. Assume that prior to multiplying row j by the constant k, you would have had to add a-times the i-th row to row j to eliminate the specific element. Since row j was multiplied by k, you now have to add a*k-times row i to row j in order to eliminate that element. Well now I'm wondering wether this is basically sufficient to prove equivalence, or whether I should use induction to prove that this is valid for all elimination steps?