A
Homework: Text p. 193-194 (#s 24,29,32-33) and p. 198 (#s 23,26)
Review: p. 204 (#s 20 a-b)
24)
29)
32)
33)
8 dimes, 17 quarters
They are equivalent
60 mL of 90% acid solution, 40 mL of 40% acid sol.
120 lbs of $10/lb beads, 80 lbs of the $15/lb beads.
23) 4.5% investment: $2,800
7.5% investment: $3,200
26) 118 yds is length and 42 yds is the width
20) a. y + 1 = 2(x - 3) or y + 3 = 2(x - 2)
b. y = 2x - 7
A
Aim #29: How do we graph the solutions to inequalities with 2 variables?
Homework: Page 148 #1 - 19
Do Now: Circle the ordered pairs that are solutions to the inequality 4x - y ≤ 10.
(2, 3)
(6, 0)
(4, -1)
(1, -6)
(-2, -18)
How many ordered pairs are in the solution set to the inequality?
Ex #1:
a) Graph the equation 4x - y = 10.
b) Does changing the equation y = 4x - 10 to the inequality y ≥ 4x - 10 change the
solution set of the graph? Why or why not?
*The graphical representation of the solution to a two variable linear
inequality is called a half-plane .*
c) Write an ordered pair that is not on the line but is still in half-plane of the
inequality y ≥ 4x - 10.
Identifying the half-plane:
• In order to clearly identify the half-plane, we must SHADE the graph in
the appropriate direction.
• To determine the appropriate shading direction, we will use a test point
from either side of the half-plane in the original inequality.
• If your coordinate satisfies the inequality, you will shade the half-plane
containing that coordinate. If not, the shading covers the half-plane not
containing that coordinate.
A
Ex #2: Let's change the inequality from:
y ≥ 4x - 10 to y > 4x - 10
a) There are still infinitely many solutions, but what ordered pairs will no longer
satisfy the inequality?
b) How do we represent that graphically?
Ex #3: Below, show the solution set to the inequalities graphically. Graph and
label the inequality and shade appropriately.
a) -3y < 6 - x
c) 7 ≥ y
b) y > 5 + 2x
d) x ≤ -2
A
e) y - 5 < 3(x + 1)
f) 3x - 4y > 16
Ex #4: At Barney's Garage, it takes an average of 1 hour for a tune-up and oil
change and an average of 6 hours to replace a transmission. If Barney, the
mechanic, puts in no more than 42 hours a week,
a) Write an inequality that describes the possible number of tune-up and oil
changes (x) and transmission replacements (y) that he can do.
b) Graph your answer to part a.
c) What is the maximum number of each he can do?
7 transmissions and 42 tune ups and oil changes
d) What is the meaning of the ordered pair (12,4)? How many hours does he have
left to attend to other mechanical tasks?
12 tune ups and oil changes, 4 transmissions
x + 6y ≤ 42
12 + 6(4) ≤ 42
36 ≤ 42
6 hours left!
A
Sum It Up:
When we represented the solution set graphically to inequalities in previous
lessons, those inequalities had one variable. With a 2 variable inequality, we can
still represent the solution set graphically, but now on a Cartesian plane or (x, y)graph.
We use a dotted line when graphing the inequalities <, > or ≠.
We use a solid line when graphing the inequalities ≤ or ≥.
Shading is used to represent the half-plane. To shade correctly, any ordered pair
except those on the dotted or solid line will allow us to determine which halfplane to shade.
Attachments
9H HW #24 ­ Systems 3 Variables ﴾Answers﴿.pdf