This is a really basic question. I want to prove the following statment:

If a linear system is changed to another by multiplying both sides of an equation by a nonzero constant, then the two systems have the same solution.

I know this is very obvious and seemingly pointless to prove. However, I never have been able to tackle the concept of proof and I can rarely figure out how to begin on things like this.

This is my linear system:

$\displaystyle a_{1,1}x_1+a_{1,2}x_2+...+a_{1,n}x_n=d_1$

$\displaystyle a_{2,1}x_1+a_{2,2}x_2+...+a_{2,n}x_n=d_2$

$\displaystyle a_{m,1}x_1+a_{m,2}x_2+...+a_{m,n}x_n=d_m$

The solution set is an n-tuple $\displaystyle {s_1,s_2....s_n}$. Where would I go from here?