You have a gift certificate to a book store worth $95. each paperback book is $10 and each hardcover book is $17. you must spend at least $20 in order to use the gift certificate. write and graph a system of inequalities to model the number of each kind of books you can buy. let x= the number of paperback books and y= the number of hardback books

You make a system of inequality to spend at least $20. The word "at least" means you can spend equal to $20 or higher than $20. Or you can write it as,
⇒ what you buy should be ≥ 20

Input the price to the inequality above
⇒ what you buy should be ≥ 20
⇒ paperback price + hardcover price ≥ 20
⇒ 10x + 17y ≥ 20

Because the number of paperback books and the number of hardcover books can't be negative, make new inequality forms
⇒ x ≥ 0
⇒ y ≥ 0

So this is the summary
10x + 17y ≥ 20
x ≥ 0
y ≥ 0