Transcript Graphing Inequalities

Graphing Inequality
Systems
Students will be able to graph systems
of inequalities in order to solve them.
Systems of Linear Inequalities
• A system of linear inequalities is a set of two
or more linear inequalities with the same
variables.
• The solution to a system of inequalities is
often an infinite set of points that can be
represented graphically by shading.
• When you graph multiple inequalities on the
same graph, the region where the shadings
overlap is the solution region.
FHS
Systems of Equations
2
Graphing Systems of Inequalities
• Solve this system of inequalities:
1

y

x 3

2

y  x  2
4
2
• For y  1 x  3 graph
5
2
a dashed boundary
-2
1
line y  x  3 and
2
-4
shade below it.
FHS
-6
Systems of Equations
3
Graphing Systems of Inequalities
• Solve this system of inequalities:
1

y

x 3

2

y  x  2
4
2
• For y  x  2 graph
a solid boundary line
y  x  2 and
shade above it.
• The overlapping region
is the solution
of the system.
FHS
5
-2
-4
-6
Systems of Equations
4
Writing the Inequalities
• Write a system of inequalities for the given
graph.
• The equation for this
boundary line would be
2
y   x 2
3
• Since the area is shaded
below the line, (0, 0)
must be a solution. Thus,
the inequality would be
2
y   x  2 First equation of system
3
FHS
Systems of Equations
5
Writing the Inequalities
• Write a system of inequalities for the given
graph.
• The equation for this
boundary line would be
y  x 3
• Since the area is shaded
below the line, (0, 0) is
not a solution. Thus, the
inequality would be
y  x 3
FHS
Second equation of system
Systems of Equations
6
Writing the Inequalities
• Write a system of inequalities for the given
graph.
• The equation for this
boundary line would be
1
y   x 3
2
• Since the area is shaded
above the line, (0, 0) is
not a solution. Thus, the
inequality would be
1
y   x  3 First equation of system
2
FHS
Systems of Equations
7
Writing the Inequalities
• Write a system of inequalities for the given
graph.
• The equation for this
boundary line would be
y  3x  3
• Since the area is shaded
to the right of the line,
(0, 0) is a solution. Thus,
the inequality would be
y  3x  3
FHS
Second equation of system
Systems of Equations
8