We know that x represents the number of trips to the airport, and y represents the number of trips from the airport. If the taxi driver had 18 fares in total, then we can express the first equation.
[tex]x+y=18[/tex]The price of a ride to the airport is $3.50 and from the airport is $9, if the driver collected $118 for the day, then we can express the second equation.
[tex]3.50x+9y=118[/tex]In order to solve this system of equations, let's solve the first equation for x.
[tex]x=18-y[/tex]Then, we combine it with the second equation.
[tex]\begin{gathered} 3.50(18-y)+9y=118\Rightarrow63-3.50y+9y=118\Rightarrow5.5y=118-63 \\ 5.5y=55\Rightarrow y=\frac{55}{5.5}\Rightarrow y=10 \end{gathered}[/tex]Once we have the value of one variable, we can easily find the value of the other one.
[tex]x=18-10=8[/tex]