Linear Inequalities
Would y > 3x - 4 have a solid or dotted boundary line?
Dotted
y = x + 4
y = 2x + 5
The solution to the system of equations:
r + s = -6
r - s = -10
What is (-8, 2)?
The solution to the system:
x = 4y
2x + 3y = 22
What is (8, 2)
Suppose you combine ignots of 25% copper alloy & ignots of 50% copper alloy to create 40kg of 45% copper alloy. What are the equations needed to solve this system?
x + y = 40
.25(x) + .50(y) = .45(40)
Is (-1, 6) a solution to the following inequality?
y < 2x + 9
Yes
The solution to the system of equations:
y = 3x - 2
y = -x - 2
What is (0, -2)?
The solution to the system:
8a + 5b = 9
2a - 5b = -4
What is (0.5, 1)?
The solution to the system
y = x - 2
3x - y = 16
What is (7, 5)
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?
True or False:
If (0,0) makes an inequality true, you shade the side of the boundary line where (0,0) is located.
True
The solution to the system of equations:
y = -3
x = 5
What is (5, -3)
The solution to the system:
2x + 3y = 6
3x + 5y = 15
What is (-15, 12)?
The solution to the system
y = 3x - 1
7x + 2y = 37
What is (3, 8)
Tickets to a football game cost $5 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. How many of each were purchased?
400 advanced tickets, 200 game-day tickets
Is the ordered pair (3, 8) a solution of the following system:
y > 2x - 4
y < -4x + 9
No
The solution to the system of equations
y = (1/3)x - 3
2x - y = 8
What is (3, -2)
The solution to the system
2a - 4b = 12
-8a + 16b = -48
What is infinitely many solutions?
The solution to the system
3s - 2t = 4
t = 2s - 1
What is (-2, -5)
Tom starts a business mowing lawns. He purchases a lawn mower for $200 and it costs him $2 in gas per lawn. Tom charges $22 per lawn. After how many lawns would Tom break even?
10 lawns
Write an inequality to represent the situation:
You are shopping for balloons to decorate for the school dance. Blue balloons cost $5/pack & white balloons cost $3/pack. You have $48 to spend.
3x + 5y <(or equal to) 48
The solution to the system of equations:
y - 3x = 3
y = 3x - 2
What is no solution?
The solution to the system:
(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4
What is (24, 8)
The solution to the system
t + u = 12
t = (1/3)u
What is (3, 9)?
Write and solve a system of equations:
The sum of two numbers is 20.
The difference between 3 times the larger number and 2 times the smaller number is 40.
x + y = 20
3x - 2y = 40
(16, 4)