Systems of
Equations Elim.
Equations Elim.
Systems of
Equations Sub.
Equations Sub.
Vocabulary
Systems of
Inequalities Graphing
Inequalities Graphing
Writing inequalities and systems of inequalities
100
x + 3y = 7
8x - 3y = 2
(1,2)
100
What is the solution to the system?
y = 2x + 2
y = x - 1
(3,-4)
100
what are 3 methods of solving systems of equations?
elimination
graphing
substitution
100
when graphing linear inequalities what does < and > mean
Use a Dotted Line
100
Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party. Write an inequality that models her situation. Let x=number of people
50 + 4x ≤ 100
200
4x - 3y = 16
5x + 3y = 20
(4,0)
200
What is the solution to the system?
y = 2x + 5
y = x + 3
(-2,1)
200
What type of solution do parallel lines have?
No Solution
200
when graphing linear inequalities what does ≥ and ≥ mean?
use a solid line
200
250x+50y<=4500
300
-2x - 9y = -25
-4x - 9y= -23
(-1,3)
300
What is the solution to the system?
3x - 2y = 8
y = 6 - x
(4,2)
300
How can you tell if a linear system has infinitely many solutions?
the equations are the same and the lines lie on top of each other
300
y<=1/2x+5
y<1/2x+5
Is (-10,0) in the solution set of the above system? Why?
No, because (-10,0) is on the dotted line of the second inequality.
300
Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2.50 and the earrings cost $4. She needs to make at least $75. Sarah knows she will sell more than 15 bracelets.
Let x= number of bracelets
y= number of earrings
2.50x + 4y ≥ 75
x + y > 15
400
The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert tickets sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?
x=8
400
What is the solution to the system?
4x - 5y = 15
8x + 5y = 45
(5,1)
400
What happens to the inequality symbol when you divide both sides by a negative number?
Flip the inequality symbol
400
Graph the system of inequalities.
y < 5x - 1
y > 3x + 12
Is (-10,-40) in the solution set? Why?
No, because (-10,-40) is not in the overlapping shaded region.
400
The band is selling boxes of fruit to raise money for new uniforms. Boxes of oranges cost $12 per box and boxes of grapefruits cost $15 per box. To get free shipping on all of the fruit each band member must sell at least 25 boxes of fruit. In order to meet your goal, you want to sell at least $500 worth of fruit. Write a system of linear inequalities to model the situation
Let x= boxes of oranges
y= boxes of grapefruit
12x + 15y ≥ 500
x + y ≥ 25