3-3 Solving Systems of Linear Inequalities
Objective
Solve systems of linear inequalities
by graphing and shading
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Example 1A: Graphing Systems of Inequalities
Graph the system of inequalities.
x – 3y < 6
2x + y > 1.5
For x – 3y < 6, graph the dashed
1
boundary line y = x – 2, and
3
shade above it.
For 2x + y > 1.5, graph the
dashed boundary line
y = –2x + 1.5, and shade above it.
The overlapping region is the solution region.
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Example 1B: Graphing Systems of Inequalities
Graph each system of inequalities.
y < –3x + 2
y ≥ –1
For y < –3x + 2, graph the
dashed boundary line
y = –3x + 2, and shade
below it.
For y ≥ –1, graph the solid
boundary line y = –1, and
shade above it.
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Example 3: Geometry Application
Graph the system of inequalities, and classify
the figure created by the solution region.
x ≥ –2
x≤3
y ≥ –x + 1
y≤4
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Example 3 Continued
Graph the solid boundary
line x = –2 and shade to the
right of it. Graph the solid
boundary line x = 3, and
shade to the left of it.
Graph the solid boundary
line y = –x + 1, and shade
above it. Graph the solid
boundary line y = 4, and
shade below it. The
overlapping region is the
solution region.
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Notes #1
1. Graph the system of inequalities.
y<
–3
y ≥ –x + 2
For y < – 3, graph the
dashed boundary line
y = – 3, and shade below
it.
For y ≥ –x + 2, graph the
solid boundary line
y = –x + 2, and shade above it.
The overlapping region is the solution region.
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Notes #2
2. Graph the system of inequalities and classify
the figure created by the solution region.
y≤
x–2
y ≥ –2x – 2
x≤4
x≥1
trapezoid
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Notes #3
3. The cross-country team is selling water
bottles to raise money for the team. The
price of the water bottle is $3 for students
and $5 for everyone else. The team needs
to raise at least $400 and has 100 water
bottles. Write and graph a system of
inequalities that can be used to determine
when the team will meet its goal.
Holt Algebra 2
3-3 Solving Systems of Linear Inequalities
Notes #3
x + y ≤ 100
3x + 5y ≥ 400
Holt Algebra 2