A high school club has a performance, with 800 tickets to sell. Tickets are $6 before the day of the show, and $9 on the day of the show. They must sell $5000 in tickets. How do I write a system of inequalities to represent the equation?

If x sold early, and y sold on the day, then

x+y <= 800
6x+9y >= 5000

To write a system of inequalities to represent the given scenario, we need to define the two conditions:

Condition 1: The total number of tickets sold multiplied by the ticket price before the day of the show should be less than or equal to $5000.
Condition 2: The total number of tickets sold should be less than or equal to 800.

Let's use the following variables:
x = number of tickets sold before the day of the show
y = number of tickets sold on the day of the show

Now we can write the system of inequalities:

Condition 1: Total ticket sales multiplied by ticket price before the day of the show should be less than or equal to $5000:
6x + 9y ≤ 5000

Condition 2: The total number of tickets sold (including both before and on the day of the show) should be less than or equal to 800:
x + y ≤ 800

So, the system of inequalities representing the given scenario is:
6x + 9y ≤ 5000
x + y ≤ 800