Answer
Basic cable service $=\$25$.
Each movie channel $=\$10$.
Work Step by Step
Let the charges for the basic cable service $=S$.
And the charges for each movie channel $=C$.
Condition 1:-
Basic cable service plus one movie channel is equal to $\$35$ per month.
$\Rightarrow S+C=35$ ...... (1)
Condition 2:-
Basic cable service plus two movie channel is equal to $\$45$ per month.
$\Rightarrow S+2C=45$ ...... (2)
Subtract equation (2) by equation (1).
$\Rightarrow S+2C-(S+C)=45-35$
Simplify.
$\Rightarrow S+2C-S-C=10$
$\Rightarrow C=10$
Substitute the value of $C$ into the equation (1).
$\Rightarrow S+10=35$
Subtract $10$ from both sides.
$\Rightarrow S+10-10=35-10$
Simplify.
$\Rightarrow S=25$.
