Math 20-1
Systems of Equations and Inequalities: Lesson #7
Linear Inequalities in 2 Variables
Objective: By the end of this lesson, you will be able to:
- Sketch the graph of a linear inequality in 2 variables
- Explain how test points can be used to determine the solution region
- Model and solve a problem with a linear inequality
If an inequality has two variables, the solution is a _____________ on the coordinate plane,
representing all the possible ordered pairs that satisfy the inequality. We can graph the solution
on a __________________ ___________ instead of a number line.
To graph a 2-variable linear inequality:
1. Find the _______________ __________.

The boundary line is ____________ if the value is included (  or  ).

The boundary line is ____________ if the value is not included (< or >).
2. Shade the ____________________ that satisfies the inequality.
 Choose a test point:

If it makes the inequality true,

If it makes the inequality false,
e.g. 1) Graph the following linear inequalities:
a) 2 x  3 y  12  0
Math 20-1
Systems of Equations and Inequalities: Lesson #7
b) x  4 y
e.g. 2) The library staff wants to buy flowers to spruce up the place. A pot of marigolds costs $5
and a pot of petunias cost $6. The maximum budget for the flowers is $60.
a) Write an inequality that represents this situation.
b) Graph the inequality.
c) Suggest a combination of pots of marigolds and petunias the library staff could buy
within their budget.
Math 20-1
Systems of Equations and Inequalities: Lesson #7
e.g. 3) An inequality whose boundary line has y-intercept 5 and x-intercept 2.5 is shown below.
Write the inequality represented by the graph.
Assignment:
p. 472-474 #4, 7, 9, 11-13, 15