To solve for the systems x-5y=10, 2x-10y=20 by elimination, first multiply the first equation by -2 which will get you to -2x+10y=-20, 2x-10y=20. Then, now that you have terms that can be eliminated, you add the two equations together:
(-2x+2x)+(10y-10y)=(-20+20)
This will result in the answer 0=0 meaning that the solutions are all real numbers.