CP Algebra I
7.6 Systems of Inequalities
Objectives:
Name: ________________________________________
Date: _________________________ Block: ________
To solve systems of linear inequalities by graphing
To model real-world situations using systems of linear inequalities
Warm-up: Graph the system of linear equations in number one and graph the inequality for
number two.
2
1) 𝑦 = 3𝑥 − 6
2) 𝑦 ≤ 3 𝑥 − 1
𝑦 = −𝑥 + 2
Key Terms:
~ Two or more linear inequalities together form a SYSTEM OF LINEAR INEQUALITIES.
~ A SOLUTION OF A SYSTEM OF LINEAR INEQUALITIES makes each inequality in the system
true.
ìï y > 2x - 5
Example 1: Solve by Graphing í
ïî 3x + 4y < 12
ìï y ³ -x + 2
Example 2: Solve by Graphing í
ïî 2x + 4y < 4
Example 3: Writing a System of Linear Inequalities
Example 4: A zookeeper wants to fence a rectangular habitat for goats. The length of the
habitat should be at least 80 ft. and the farmer can only afford 310 ft. of fencing. What are the
possible dimensions of the habitat?
Example 5: Suppose you want to fence a rectangular garden plot. You want the length of the
garden to be at least 50 ft. and the perimeter to be no more than 140 ft. Solve by graphing to
show all of the possible dimensions of the garden.
HW: pg. 414-415 #1-3, 4-22 even
Optimal Solutions (This is how the people use this stuff!) [A preview to Algebra II]
Example 5: farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres.
However, he has only $1200 to spend and each acre of wheat costs $200 to plant and each
acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours
and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the profit
is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted
to maximize profits?
Example 6: In order to ensure optimal health (and thus accurate test results), a lab technician needs
to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates,
and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.
Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and
blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein
per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of
protein per ounce, at a cost of $0.30 per ounce.
What is the optimal blend?
HW: p 414 – 415; 1 -3, 4-24 even