### Systems of Inequalities

```Warm Up
• Solve the following system of equations using
any method:
ìï y = 3x - 2
í
ïî x + y = -6
Word Problems
• When working with system-of-equations word
problems, determine the two equations that
you can write.
• Then solve using any method
Example 1
• A test has twenty questions worth 100 points.
The test consists of True/False questions
worth 3 points each and multiple choice
questions worth 11 points each. How many
multiple choice questions are on the test?
Example 2
• The senior classes at Knightdale High School
and Enloe HS planned separate trips to New
York City. The senior class at KHS rented and
filled 1 van and 6 buses with 372 students.
EHS rented and filled 4 vans and 12 buses with
780 students. Each van and each bus carried
the same number of students. How many
students can a van carry? How many students
can a bus carry?
Example 3
• Matt and Ming are selling fruit for a school
fundraiser. Customers can buy small boxes of
oranges and large boxes of oranges. Matt sold
3 small boxes of oranges and 14 large boxes of
oranges for a total of \$203. Ming sold 11 small
boxes of oranges and 11 large boxes of
oranges for a total of \$220. Find the cost each
of one small box of oranges and one large box
of oranges.
We show the solution to a linear
inequality with a graph.
Step 1) Put the inequalities into slopeintercept form.
slope
y = mx + b
y-intercept
Step 2)
Graph the line
a) If the inequality is < or >, make the
lines dotted.
b) If the inequality is < or >, make the
lines solid.
Step 3)
Shade the correct region of the graph:
a) Above the line for y > or y .
b) Below the line for y < or y ≤.
**This is because more
then 1 ordered pair can be
a solution!
Examples:
1) y > -5x + 4
Examples:
2) x < 4
3) y ≥ -3
Examples:
4) 2x – 3y ≤ 6
Careful when you
divide by a
negative!
Examples:
5) 3x + 2y < -2
We show the solution to a
system of linear inequalities
with a graph!
Steps to Graphing a System of Inequalities:
1) Put the inequalities into slopeintercept form.
2) Decide if the lines should be dotted or
solid.
3) Shade above for y > or y , shade
below for y < or y ≤.
4) Shade the overlapping section darker
to show where the solutions to both
inequalities lie.
Example #1:
a: 3x + 4y > - 4
b:
x + 2y < 2
Put in Slope-Intercept Form:
Graph each line, make dotted or solid
and shade the correct area.
a : y  
3
x 1
4
dotted
b : y  
1
x 1
2
dotted
#2 Graph the system of
linear inequalities.
x  –1
y>x–2
#3
x > -2
y<6
-2x + y > -5
Class Work
• Graph the System of Inequalities on the
handout
Homework
• HW 2.4
```