Algebra 1-1 DA

Ch 5 Notes - Solving Systems of Linear Inequalities

Two or more linear inequalities form a______.

The ______to a system of linear inequalities lie in the overlapping region of the graphs of both inequalities or lie on a solid line if one or both of the inequalities contain  or ≥.

**Reminder** The boundary line:

Dashed if the inequality is < or > Shade above if y > or y ≥

Solid if the inequality is  or ≥Shade below if y < or y 

Example 1 – Graph the system of linear inequalities:
a.) y ≥ 2
x < 3
/ b.) y < 2x + 1
y ≥ x

c.) y≤ -x + 4
y 3x + 1
/ d.) y ≤ -½x + 2
y≤ 2x – 2

Example 2 – Graph the system of linear inequalities:
a.) x + 2y 2
y-1/2x – 2
/ b.) 2x – 3y3
3y2/3x + 12

c.) x – 2y 4
y> 2x + 2
/ d.) 4x + 2y ≥ -6
y-8x + 3

Example 3 – Write a system of inequalities to describe the shaded area of the graph.
a.)
/ b.)
/ c.)

Example 4 - Decide whether the following ordered pairs are solutions to the system of linear inequalities.
a.)
(6, -2)
(-3, -1)
( 0, 3)
(-8, 6)
(4, 4)
(-4, 4 ) / b.)
(6, -2)
(8, 2)
( 10, -5)
(8, -4)
(3, -3)
(10, 1 )
Example 5 – Writing an inequality from a word problem
a) Suppose you intend to spend no more than $60 buying books. Hardcover books cost $12 and paperback cost $5. How many books of each type can you buy? / b) Suppose your class is raising money for the Red Cross. You make $4 on each basket of fruit and $5 on each box of cheese that you sell. How many items of each type must you sell to raise more than $100?
Example 6 – Writing a system of inequalities from a word problem
a) You can work a maximum of 40 hours a week. You need to make $400 in order to cover your expenses. Your office job pays $12 an hour and your babysitting job pays $10 an hour. Let x represent the number of hours spent working your office job and y represent the number of hours spent babysitting. / b) Marsha is buying flowers and shrubs to plant in her garden. The flowers cost $4 each, and the shrubs cost $10 each. She wants to buy at least 5 plants and can spend no more than $100. Let x represent the number of flowers and y represent the number of shrubs. Write a system of linear inequalities to model the situation.
Example 7 – Writing and graphing a Linear Inequalities Application
Fuel from QT cost $2 per gallon and fuel from BB costs $2.50 per gallon. You have at most $25 to spend on fuel from both QTand BP.

a.) Write an inequality to represent this scenario.

b.) Graph

c.) Give 2 possible combinations of gas from QT and BP.

Example 8– Writing and graphing a System of Linear Inequalities Application
You are ordering bricks and sand. You need a minimum of 400 bricks and 10 bags of sand. Bricks weigh 3 lb each and sand weighs 30 lb per bag. The maximum weight that can be delivered in a truck is 3000 lb. Let x represent the number of bricks and y represent the number of bags of sand.

a.) Write and graph a system of linear inequalities that
shows how many bricks and bags of sand could be ordered.
b.) Can 600 bricks and 30 bags of sand be delivered?
c.) Can 500 bricks and 60 bags of sand be delivered?