2.  Systems of linear inequalities are used all over, from animal conservation efforts to trying to decided how many gifts to buy.

3.  Suppose you want to decide how many gifts you will buy for family and friends.  You can use a system of linear inequalities to help you decide on a good solution.

4.  Suppose you want to buy between 3 and 5 gifts for your 2 family members and 3 friends.

5.  You can represent this problem as two inequalities, shown below.

6.  You can graph the inequalities to find solutions for how many different ways you can buy presents.

7. y + x + 1 2 3 4 5 1 23 4 5 -5 -4-3 -2 -2

8.  The region where there is some overlap is where the solutions of the system of inequalities lie.

9. y + x + 1 2 3 4 5 1 23 4 5 -5 -4-3 -2 -2

10.  Only the solutions which lie in the first quadrant can be used to decide how many gifts to by, since you cannot give a negative gift.

11.  Only solutions having whole numbers are useful solutions, since you cannot give a partial gift.

12. y + x + 1 2 3 4 5 1 23 4 5 -5 -4-3 -2 -2 Red dots represent the actual solutions. Buying just for family members Buying for family and friends Buying just for friends

13.  You could by 1 present for each of your friends and none for your family.  You could by 2 presents for each of your family members and none for your friends.  You could buy 1 present for each of your friends and family members.