Coordinate Algebra: Unit 2
Name___________________
Date_________________
Lesson 10: Solving Systems of Inequalities
Period________
Guided Notes
Standard and Skills
A.REI.12 Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of
a strict inequality), and graph the solution set to a system of linear inequalities in two variables as
the intersection of the corresponding half-planes.
SWBAT graph a linear inequality on a coordinate plane
SWBAT graph a systems of linear inequalities and find a solution
Part I: Graphing Inequalities
Graphing Linear Inequalities
Step 1: Graph the ___________________, which is the equation of the line.
Step 2: By looking at our ________________________, determine how to draw the line.
> or < will give us a _____________________ line.
 or  will give us a _________________ line.
Step 3: Determine which side of the boundary to __________________ in order to represent
our__________________________________.
 
How do we know which side of the boundary to shade?
Step 1: We must pick an ordered pair to _____________________.
Step 2: We must _______________________ the ordered pair into our inequality to determine if it makes a
_________________ statement or a ___________________ statement.
Step 3: If our statement is true we will shade _____________________ the point. If our statement is false we will shade
____________________ the point.
Example 1: Graph the inequality.
y > -3x + 2.
Name two possible solutions for the system.
Guided Practice
Graph and shade the following inequalities. Name 2 possible solutions for each system.
1. y  3x  4

2. y  2x 1

3. y  4 x  2

4. 2y  2x  12
(Put in y = mx+b form)

Part II: Solving Systems of Inequalities
We have learned that the solution of a linear system of equations occurs where the two lines
_______________________________. Likewise, the solution of system of linear inequalities occurs where the two regions
_________________________. Any ordered pair that lies in the _______________________________ is a solution.
Steps to Solving Systems of Inequalities
Step 1: Put all inequalities in ______________________ form.
Step 2: Graph the _______________________.
Step 3: Shade the ____________________ for each inequality. (Use different colors for each. Darken the region where
color overlaps.) The overlap of the two regions is your SOLUTION!
Example 1. Solve the system of inequalities.
 y  3x  6

 y  4 x  2
Example 2: Solve the system of inequalities.
 x  2y  6

3

 y   2 x  5
Independent Practice
Solve each linear system of inequalities by graphing. Make sure to show your region of solution and identify at least two
solutions to the system.
 y  2x  4
 x  3
1. Solve 
 y  2x  2
y   x  1
2. Solve 
y  3

3. Solve 
1
 y  2 x  1
x  y  2
 y  2x  1
4. Solve 
5. Solve
2x  y  4
2 x  y  4
6. Solve
y>
2
x 2
3
2
y < x 1
3