Download Lesson 27b

Name
Class
M1.C.21 Solution sets to Inequalities in Two Variables
Algebra 1
Recall: Inequalities in one variable are graphed on a number line, using open or closed circles and
arrows.
Objectives: Students will be able to recognize and identify the solution to an inequality with two
variables. They will be able to graph the inequality and correctly interpret the solution based on
the symbol.
For the inequality in #1 and #2, circle the ordered pair(s) that is a solution.
1.
3x + y < 10
a.
2.
(2, 4)
b. (0, 8)
c. (5, -7)
d. (3, 6)
b. ( -1, -5)
c. ( 2, -2)
d. (4, 0)
-2x + y ≥ -6
a.
(3, 4)
For question 3, fill in the blanks with the best answer.
3. Graphs of an inequality in one variable are graphed on a ______________________.
If the number is a solution use a(n) ________________ circle.
If the number is not a solution use a(n) _____________________circle.
Graphs of an inequality in two variables are graphed on a _______________________.
The points on the graph form a _____________________.
If the points on the line are in the solution, the line is ____________________.
If the points on the line are not in the solution, the line is ____________________.
4. a) Write an inequality to represent this situation:
“The difference of two numbers is less than 9.”
b) Find three solutions when x = 3.
5. a) Graph the inequality x + y < 6.
b.
Using your graph, determine which of the following points are solutions:
(1, 8)
(4, 4)
(5,1)
(9,0)
(6, -2)
(--3,6)
6. Shelly is making cookies, chocolate chip and oatmeal. She has to make at least 60 cookies.
a)
Create an inequality to represent this situation.
b)
Create a table of values.
c)
Construct a graph.
d)
Her recipes result in batches of cookies by the dozen. How many solutions result in
even dozens for the types of cookies?
Look at each graph then choose the best description.
7. a.
b.
a) The half plane x < 2
a) The half plane x < -3
b) The half plane x > 2
b) The half plane x > -3
c) The half plane y < 2
c) The half plane y < -3
d) The half plane y > 2
d) The half plane
8.
y > -3
Match the inequality with the description of the solution.
_______ 1. The half plane to the right of the line
a. x < -2
including the line.
_______ 2. The half plane below the line not
b. y < -5
including the line
_______ 3. The half plane above the line including
c. x ≥ 3
the line.
________4. The half plane to the left of the line not
including the line.
d.
y≥1