Answer
See below.
Work Step by Step
Let $x$ be the cost of a basic cable service and $y$ be the cost of a channel, then our two equations are $x+y=35,x+2y=45$, so if I subtract the first equation from the second one I get $y=10$ and then $x=35-y=25$, so the basic price is $25$ and the cost for a channel is $10$.
