Hi, can anyone help me explain why these actions do not change the solution set of a system of equations?

i. Multiplying one equation by a non-zero number

ii. Adding one equation to another

How do I explain this if S is the solution set of the system of m equations with the unknowns $\displaystyle x_{1}, x_{2}, ... , x_{n}$ and $\displaystyle \overline{s} = s_{1}, s_{2}, ... , s_{n} \in S$ where if each equation in the system is satisfied, then $\displaystyle x_{1} = s_{1} , ... , x_{n} = s_{n}$

Thank you.