Let 
be the number of lower-level tickets sold, and 
the number of upper-level tickets sold.
Now, if the theater sells 350 tickets total, that means the number of lower-level and upper-level tickets that got sold should add up to 350, so one equation in the system is
You also know that the theater earns $10250 in sales, so if each lower-level ticket costs $35, and each upper-level ticket costs $25[/tex], this means
represents the amount of money made from selling lower-level ticekts, and 
represents the amount of money made from selling upper-level tickets. You get the second equation in the system,
So the system is
Any one of the methods listed in the second part works in solving this system (though I'm not sure what "variable" refers to), but I think substituting involves the least work.
Solve the first equation for either variable; I'll choose.
Now substitute this into the second equation for, then solve for .
So 200 upper-level seats were sold. Meanwhile, since, this means
so that 150 lower-level tickets were sold.
Now, if the theater sells 350 tickets total, that means the number of lower-level and upper-level tickets that got sold should add up to 350, so one equation in the system is
You also know that the theater earns $10250 in sales, so if each lower-level ticket costs $35, and each upper-level ticket costs $25[/tex], this means
So the system is
Any one of the methods listed in the second part works in solving this system (though I'm not sure what "variable" refers to), but I think substituting involves the least work.
Solve the first equation for either variable; I'll choose
Now substitute this into the second equation for
So 200 upper-level seats were sold. Meanwhile, since
so that 150 lower-level tickets were sold.