Hi, first post here. I need help with a proof from linear algebra.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: Linear algebra proof problem

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