Here is the problem I have. It seems like I just have to use some of the properties from the book to solve this but I can't wrap my head around it.

Let A be a 3 x 4 matrix, letv1andv2be vectors in R3, and letw=v1+v2. Supposev1= Au1andv2= Au2for some vectorsu1andu2in R4. What fact allows you to conclude that the system Ax=wis consistent?

What I have calculated so far based on algebraic rules for matrices:

w=v1+v2 =Au1 +Au2= A(u1 +u2), sou1 +u2=x.

I know a system is consistent only if it has a solution, so that's what I'm trying to prove. But this is very abstract so I'm not sure where to begin. I feel like it has something to do with multiplying A byxbut I'm not really sure. Does anyone have some tips or hints?