Download A2 – Section 2

A2 – Section 2.8
Date______________
Inequalities in Two Variables
Inequality in two variables: any function using x and y that has an _____________
instead of an equal sign to relate the two sides
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Usually, there are _______ solutions to inequalities in two variables, which will
be ordered pairs.
You will need to _______ half of the graph, called a half-plane, to show all of
the solutions.
You will need to consider if the boundary line should be included in the solution
graph. (You’ll use a solid line if the boundary line is included,)
Ex 1 Check to see if the following ordered pairs are solutions of 5x + 8y > 23.
a) (-2, 6)
b) (3, 1)
c) (4, -5)
Boundary lines:

________ boundary lines mean that the boundary line is included in the solution
set. Use a solid line for < or >.
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_________ boundary lines mean that the boundary line is NOT included in the
solution set. Use a dashed line for < or >.
Ex 2 Use the graph at the right to determine
if the following points are solutions of the
inequality represented by the graph.
a) (2, -4)
b) (3, 4)
c) (5, 0)
d) (1, 3)
Graphing Inequalities in Two Variables:
1.
Graph the _______________________
Dashed if __________________
Solid if ____________________
2.
Test a point not on the line to see if that half-plane is a solution to the
inequality. Use _______________ if possible!
3.
4.
If it is a solution, _________ the half-plane containing that point. If it is
NOT a solution, ________ the other half-plane.
ALL LINEAR INEQUALITIES MUST HAVE __________________ in their
graphs!!
Ex 3 Graph the following inequalities.
a) y < -⅜x + 5
Is (5,2) a solution? ___________
b) x > 6
Is (6,3) a solution? _________________
You Try!!
c) 4x – 7y > 28
d) y < -5x + 4
e) y > 2
f) y < 3x
Is (4,-4) a solution? _________
Is (5,5) a solution? _____________
Ex 4 The memory card of your digital camera has 256 megabytes of memory. Each
photo uses either 1 megabyte or 2 megabytes, depending on low or high resolution
photos. Write an equation that models the number of photos that can be stored on the
card when you take photos of both resolutions. What are three possible solutions?
a) Equation?
b) Solutions?
You Try!!!
A pizza shop has 300 pounds (4800 ounces) of dough. A small pizza use 12 ounces of
dough and a large pizza uses 18 ounces of dough. Write an inequality describing the
possible numbers of small and large pizzas that can be made. Then give three possible
solutions.
a) Equation?
b) Solutions?
Ex 5 You have $200 to spend on CDs and videos. CDs cost $15 each and videos cost
$20 each. Write a linear inequality to represent the number of CDs and videos you
could buy and graph the inequality.
Variables:
Linear Inequality:____________________________
Graph: