3.3 Graphing and Solving Systems of Linear Inequalities

1
3.3 Graphing and Solving Systems of Linear
Inequalities
2
Objectives/Assignment

• Graph a system of linear inequalities to find the
  solutions of the system.
• Assignment 13-49 odd

3
The following is a system of linear inequalities
in two variables
Is (0,0) a solution for this system??
(3, -1) is a solution for this system.
The graph of a system of linear inequalities is
the graph of all solutions of the system.
A solution of a system of linear inequalities is
an ordered pair that is a solution of each
inequality in the system.
4
Is (1,1) a solution to this system?
No
5
Graph the system and locate all the solutions.
Graph the line y -3x -1 and divide the plane
into 2 half-planes.
(5,0)
Test a point (like (5,0)) in one of the half
planes to decide which half-plane to shade as
solutions.
This Region
Graph the line y x 2 (Make it dashed. (Why?)
yx2
Test a point to decide which half-plane to shade.
The set of all solutions is where the two
half-planes intersect.
y -3x - 1
6
Is (3,2) a solution to this system?
Yes
7
Graph this system of Three Inequalities.
X0
y0
The Region where all three half-planes intersect,
is the set of solutions.
8
Graph the system
Name an ordered pair that is a solution to this
system.
Name an ordered pair that is NOT a solution to
this system.