Graphs of Inequalities
Infinite, One and Many Solutions
Choosing Coordinates
Equations for Tables
Understanding Graphs
100
What would change on the graph if it was: y < x + 2
The line would be dotted not solid
100
x + y = 5
x + y = -5
How many solutions would this system of equations have?
none
100
2x + y = 11
Which coordinate pair would make a true equation?
(1, 8) (2, 4) (3, 5)
(3,5)
100
x y
0 4
1 3
2 2
Which equation matches the table?
x + y = 4 xy = 4 y - x = 4
x + y = 4
100
This graph represents the budget for a trip to the zoo.
The equation is : 12x + 8y = 240
What is the budget constraint?
$240
200
What would change if it was: y > x + 2
It would be a dotted line with shading above the line
200
2x + 3y = 10
4x + 6y = 20
How many solutions would this system have?
infinite
200
Rides are $2 and games are $3, budget is $50
2x + 3y = 50
If you ride 10 rides, what coordinate pair makes the equation true?
(10, 10)
200
x y
7 10
4 7
-3 0
Which equation matches the table?
y + x =3 y - x = 3 xy = 3
y - x = 3
200
This graph shows the combination of adults and children that can attend the trip. Identify the variables.
Children cost $8 , adults cost $12
x = number of adults
y = number of children
300
The graph shows the combination of children and adults that can attend a trip.
Where would a coordinate that has more adults and children than are allowed on the trip be found?
Above the line
300
2x + 5y = 10
4x +?y = 20
What is the value of the ? to make this system have infinite solutions?
? = 10
300
Rides are $2 and games are $3, budget is $50
2x + 3y = 50
If you play 8 games, what coordinate pair makes the equation true?
(13, 8)
300
Cars (x) Trucks (y)
0 50
50 0
40 10
Based on the table, what total number of cars and trucks combined are allowed?
50
300
This graph shows the combination of adults and children that can attend the trip.
If no children go how many adults can go?
20 adults
400
A student tested (0, 0). Is it a solution to the system?
Explain.
No, because (0,0) is located outside of the shade area of the system solutions.
400
12x + 9y = 30
?x + 3y = 10
What value can replace the ? to make infinite solutions?
? = 4
400
x > y
x < y + 5
Which coordinate pair would satisfy this system?
(4, 2) (6, 2) (10, 2)
(6, 2)
400
Cars (x) Trucks (y)
0 50
50 0
40 10
Based on the table, if there were 35 cars, how many trucks would be allowed?
15 trucks
400
This graph shows the combination of adults and children that can attend the trip.
If no adults go how many children can go?
30 children
500
Write an equation for this inequality.
X > 4
500
2x + 6y = 12
x - 6y = 3
How many solutions does this system have?
one solution
500
x > y
x > -y + 3
Which pair of coordinates would satisfy this system?
(5, 3) (5, -3) (-5 , 5)
(5, 3)
500
Cars (x) Trucks (y)
0 50
50 0
40 10
Write an equation for the combination of trucks and cars based on the constraint.
x + y = 50
500
This graph shows the combination of adults and children that can attend the trip.
Children cost $8 , adults cost $12, budget = $240
If 3 children do not go, how many more adults can go?
2 additional adults
because 3 x 8 = 24 and 2 x 12 = 24