Linear Non Linear Systems of Equations by jennyyingdi

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• pg 1
```									Linear & Non-Linear Systems of
Equations
Graphing Linear Inequalities in
Two Variables
Learner Outcome 1.1
The Boundary Line

y=x
All the points on the
line of y = x, satisfy
the equation y = x.
(5, 5)

(0, 0)

The boundary line divides
(-5, -5)       the coordinate plane into
two regions.
The Region ABOVE
For every point in the region
above the boundary line, y > x.         y=x
(-10, 7)

(-5, 5)
(-15, 4)

(-10, 1)

(-15, -3)

(-12, -5)
The Region BELOW
(14, 7)

(10, 4)

(2, -2)

(10, -5)
For every point in
(-7, -8)    the region below the
boundary line, y < x.
The Boundary Line
• The boundary line for an inequality may be
solid or broken.

Broken Line
Solid Line

y>x+3                        y>x+3
y = x + 3 is part            y = x + 3 is not part
of the solution.             of the solution.
• If you have y > or ≥, you shade ABOVE
• If you have y < or ≤, you shade BELOW

Example:
• Graph: - 4x + 3y > 12
• Use a test point to check if you shaded
the appropriate region.
Word Problems

Example:
The library staff wants to plant flowers on the boulevard.
During a sale at the greenhouse, a flat of marigolds costs \$5
and a flat of petunias costs \$6, including tax. The library
staff can spend a maximum of \$60.
a. Write an inequality to describe the numbers of flats of
marigolds and flats of petunias they can buy.
b. What are the restrictions on the variables?
c. Graph the inequality.
d. Use the graph to find four possible combinations of flats of
marigolds and petunias the staff could buy (assume only
whole flats can be bought).
HOMEWORK:
Page 75
#2-34 even, 35-37, 41-45

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