Download Graph a System of Linear Inequalities

Avon High School
Section: 8.5
ACE COLLEGE ALGEBRA II - NOTES
Systems of Inequalities
Mr. Record: Room ALC-129
Semester 2 - Day 8
Graphs of Linear Inequalities in Two Variables
Graphing a Linear Inequality in Two Variables
1. Replace the inequality symbol with an equal sign and graph the corresponding linear
equation. Draw a solid line if the original inequality contains a  or  symbol. Draw a
dashed line if the original inequality contains a  or  symbol.
2. Choose a test point from one side of the half-planes. (Do not choose a point on the line.)
Substitute the coordinates of the test point into the inequality.
3. If a true statement results, shade the half-plane containing this test point. If a false
statement results, shade the half-plane not containing this test point.
Example 1
Graphing a Linear Inequality in Two Variables
Graph 4 x  2 y  8 .
Let
be positive real numbers with
, and let p be any real number.
The logarithm of a number with an exponent is the product of the exponent and the logarithm
of that number.
Example 2
Graphing a Linear Inequality in Two Variables
3
Graph y   x .
4
Example 3
Graphing a Linear Inequality without Using Test Points
a. Graph y  3
Systems of Inequalities in Two Variables
Example 4
Graph a System of Linear Inequalities
Graph the solution of the system.
x  3y  6
2 x  3 y  6
Example 5
Graph a System of Inequalities
Graph the solution of the system.
y  x2  4
x y 2
b. Graph x  2 .
Example 6
Graph a System of Inequalities
Graph the solution of the system.
x y 2
2  x  1
y  3
Example 7
Graph a System of Absolute Value Inequalities
Rewrite each inequality in the system without absolute value bars.
Then graph the rewritten system.
x 4
y 5