1. Linear & Non-Linear Systems of Equations
Graphing Linear Inequalities in Two Variables
Learner Outcome 1.1

2. 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
the coordinate plane into
two regions.
(-5, -5)
Boundary Line

3. The Region ABOVE y = x Boundary Line For every point in the region
above the boundary line, y > x.
y = x
(-10, 7)
(-5, 5)
(-15, 4)
(-10, 1)
(-15, -3)
Boundary Line
(-12, -5)

4. The Region BELOW y = x Boundary Line (14, 7) (10, 4) (2, -2) (10, -5)
For every point in
the region below the
boundary line, y < x.
(-7, -8)

5. The Boundary Line y > x + 3 y > x + 3
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
of the solution.
y = x + 3 is not part
of the solution.

6. Shading 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.

7. 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.
Write an inequality to describe the numbers of flats of marigolds and flats of petunias they can buy.
What are the restrictions on the variables?
Graph the inequality.
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).

8. HOMEWORK:
Page 75
#2-34 even, 35-37, 41-45