Hi, first post here. I need help with a proof from linear algebra. It states: suppose that (x,y)=(r,s) is a solution of: system of equations #1 ax+by=p cx+dy=q and that (x,y)=(u,v) is a solution of: system of equations #2 ax+by=0 cx+dy=0 prove that (x,y)=(r+u , s+v) is a solution for system of equations #1 . The attempt at a solution ar+bs=p cr+dy=q au+bv=0 cu+dv=0 au+bv=cu+dv i then tried solving for a,b,c and d and plugging them back into the first system of equations, however after doing so my equations become very long and confusing. I tried working it backwards but i still seem to get stuck. There has to be a simpler way of solving it but i cant seem to figure it out.