Systems of Inequalities
This method must be used to solve a system of INEQUALITIES.
What is graphing
Where is the solution of a system of equations found (cough cough, or not found) when graphed?
At the point of intersection or the lack of intersection.
The solution to the system of equations:
x + y = -6
x - y = -10
What is (-8, 2)?
x = 4y
2x + 3y = 22
The sum of two numbers is 104. Their difference is 68. What are the numbers?
What are 86 and 18?
Graph the solution set of y < 3x + 4 and y > -1/2x - 2
Ms. Cook says...?!?!
y = 3x - 2
y = -x - 2
The solution to the system:
8x + 5y = 9
2x - 5y = -4
What is (0.5, 1)?
y = x - 2
3x - y = 16
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
What is $30?
Graph the solution to the system y < x + 2 and x > 3
Ms. Cook says...?!?!
The solution to the system of equations:
y = -3
x = 5
What is (5, -3)
2x + 3y = 6
3x + 5y = 15
y = 3x - 1
7x + 2y = 37
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.00 if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
What is 400 advanced tickets, 200 game-day tickets?
You need at least 3 pounds of fruit to make muffins. Blueberries cost $4 per pound, strawberries cost $3 per pound and you can spend at most $21 on fruit. How many pounds of blueberries and strawberries can you buy?
Write a system of inequalities and graph.
Ms. Cook says...?!?
y = (1/3)x - 3
2x - y = 8
The solution to the system
- 4y = 12 - 2x
-8x + 16y = -48
What is infinitely many solutions?
The solution to the system
3x - 2y = 4
y + 1 = 2x
What is (-2, -5)
Carson wants to make 20 pounds of trail mix using nuts and chocolate chips. His budget requires that the trail mix costs him $7.60 per pound. Nuts cost $9.00 per pound and chocolate chips cost $2.00 per pound. How many pounds of nuts and how many pounds of chocolate chips should he use?
16 pounds of nuts and 4 pounds of chocolate chips
You can work a total of no more than 10 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $56 each week to pay your bills. How many hours can you work at both of your jobs?
Write a system of inequalities and graph.
Ms. Cook says...?!?
y - 3x = 3
y = 3x - 2
The solution to the system:
(1/3)x + (1/4)y = 10
(1/3)x = 4 + (1/2)y
What is (24, 8)
The solution to the system
x + y = 12
x = (1/3)y
What is (3, 9)?
Sasheena is a lab assistant at her community college. She needs to make 200 milliliters of a 40% solution of sulfuric acid for a lab experiment. The lab has only 25% and 50% solutions in the storeroom. How much should she mix of the 25% and the 50% solutions to make the 40% solution?
80 ml of the 25% solution with 120 ml of the 50% solution