1. Lesson Objective: I will be able to …
Graph and solve systems of linear inequalities
in two variables
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples
After School Review Monday 12/12

2. Page 30
A system of linear inequalities is a set of two or more linear inequalities containing two or more variables.
The solutions of a system of linear inequalities consists of all the ordered pairs that satisfy all the linear inequalities in the system.

3. Example 1: Identifying Solutions of Systems of Linear Inequalities
Page 31
Tell whether the ordered pair is a solution of the given system.
y ≤ –3x + 1
(–1, –3);
y < 2x + 2
(–1, –3)
(–1, –3)
y ≤ –3x + 1
y < 2x + 2
–3 –3(–1) + 1 – – ≤ 
–3 –2 + 2 –
< 
– (–1) + 2
(–1, –3) is a solution to the system because it satisfies both inequalities.

4. Example 2: Solving a System of Linear Inequalities by Graphing
Page 31
Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions.
(–1, 4)
(2, 6) 
y ≤ 3
y > –x + 5 
(6, 3)
(8, 1)
y ≤ 3
y > –x + 5
Graph the system.
(8, 1) and (6, 3) are solutions.
(–1, 4) and (2, 6) are not solutions.

5. (–3, 1) and (–1, –4) are not solutions.
Your Turn 2
Page 32
Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. 
(3, 3)
(4, 4)
y ≤ x + 1
y > 2
(–3, 1) 
(–1, –4)
y ≤ x + 1
y > 2
Graph the system.
(3, 3) and (4, 4) are solutions.
(–3, 1) and (–1, –4) are not solutions.

6. Example 3: Graphing Systems with Parallel Boundary Lines
Page 32
Graph the system of linear inequalities.
y ≤ –2x – 4
y > –2x + 5
This system has no solutions.

7. Example 4: Graphing Systems with Parallel Boundary Lines
Page 32
Graph the system of linear inequalities.
y > 3x – 2
y < 3x + 6
The solutions are all points between the parallel lines but not on the dashed lines.

8. Example 5: Graphing Systems with Parallel Boundary Lines
Page 33
Graph the system of linear inequalities.
y ≥ 4x + 6
y ≥ 4x – 5
The solutions are the same as the solutions of y ≥ 4x + 6.

9. Homework
Assignment #37
Holt 6-6 #17-20, 25, 26, 35, 39