If u-v=0, they must be both the same number. Therefore, u=v. 7u+v=0. 7u is 7*u but we must get the answer reduced to 0 so u=0. We already know from the first sentence that u=v. In conclusion, both variables are equivalent to 0.
Adding v to both sides of the first equation, we have that u=v. Substituting this into the second equation, we have that 8u=0, and thus that u=0. Since u=v, we have v=0, so our solution is u=0, v=0.