Write a system of linear equations in two variables whose solution satisfies the problem. Then solve it symbolically and graphically. 1400 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $30 for covered pavilion seats and $15 for lawn seats. Total receipts were $30 comma 000. How many of each type of ticket were sold?

let

c = the number of covered pavilion tickets sold

l = the number of lawn seats tickets sold

one evening 1400 concert tickets were sold

c + l = 1,400

total receipts were $30,000

30c + 15l = 30,000

by solving the system of equations

c + l = 1,400

30c + 15l = 30,000

we find

c = 400 covered pavilion seats

l = 1,200 lawn seats

by plugging the correct numbers into each other