6.1 Solving One-Step Linear Inequalities x + 8 > 1
6.2 Solving Multi-step Linear Inequalities 5x – 3 > 12
6.3 Solving Compound Inequalities -5<2x + 3 < 7
6.4 Solving Absolute-value Equations and Inequalities
|x-4|=8
|5x+1|+3 =14
6.5 Graphing Linear Inequalities in Two Variables
Graph x + y > 3
6.6 Stem and leaf plots; mean, median, mode
6.7 Box and whisker plots
Ch 7 Systems of Linear Equations and Inequalities
November 28 A
7.1
29 A
7.2
30 H
7.3
December 1 D
7.3
2 A
Quiz 7.1-7.3
new7.4
5A
7.4
6 Penance
Service
7.5
7 Penance
Service
7.6
8 Mass
7.6 & review
9A
12 A
Chapter Review
13 A
14 H
Chapter 7 Test Review for final
15 D
Review for
final
16 A
Review for final
21 Final Exam
Ch 1-7
Due Tuesday
Due Wednesday
Due Thursday
Due Friday
11/29
11/30
12/1
12/2
7.1 p401 12,16,18, 22,26,36,44
7.2 p408-411 #14,16,18,20, 26, 30,35,44,48-51
7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44
7.3 p414 #45-52, 56; p417 1-9
7.1 Solving systems of linear equations by graphing:
Graph-Estimate-Check
y=3x-12 and y=-2x+3
(3,-3)
7.1 p401 12,16,18, 22,26,36,44
7.1 Solving a System of Linear Equations by Graphing
7.2 Solving a System of Linear Equations by Substitution
Solve by Substitution 3x+y=5 and 2x-y=10
(3,-4)
Solve by Substitution 2x+6y=15 and x=2y
(3,3/2)
Solve by Substitution x+2y=4 and –x+y=-7
(6,-1)
Homework: p408-411 #14,16,18,20, 26, 30,35,44,48-51
7.1 Solving a System of Linear Equations by Graphing
7.2 Solving a System of Linear Equations by Substitution
7.3 Solving Linear Systems by Linear Combination
Solving by graphing can be challenging
Substitution is easier than graphing, but sometimes it is not easy to
isolate the variable.
…let’s try Linear Combination
-x+2y=-8 x+6y=-16
x+6y=-16
8y=-24
y=-3
To find x, plug in -3 into one of the equations
x+6(-3) = -16 x-18=-16 x=2 solution (2, -3)
Check -2+2(-3)=-8
Solve by linear combination:
5x-4y=3 2x+8y=-2
Solve by linear combination:
3x-6y= -12
-x+3y=6
2(5x)-2(4y) = 2(3) (multiply first equation
3x -6y= -12
-3x+9y= 18 (multiply each term by 3)
3y=6
y=2
by 2 to get y’s to cancel)
10x -8y
2x + 8y
12x = 4
x= 1/3
=6
= -2
To find y: 2(1/3)+8y= -2
2/3 +8y = -2
8y=-2 2/3
8y= -8/3
y=-1/3
Check: 5(1/3) -4(-1/3) = 3
2(1/3) +8(-1/3)= -2
Solution: (1/3, -1/3)
To find x: 3x-6(2)= -12
3x=0
x=0
Check: -(0) +3(2) = 6
3(0)-6(2)=-12
Solution: (0,2)
Solve by linear combination:
2u=4v+8 3v=5u-13
2u-4v=8
-5u+3v= -13 (reorganize so variables on same side)
10u – 20v =40 (to get “u” to cancel, multiple top equation by 5)
-10u +6v = -26 (to get “u” to cancel, multiple bottom equation by 2)
-14v=14
v=-1
2u=4(-1)+8
2u=4
u=2
(to find “u”, plug in v=-1 into one of the equations)
Check: 2(2)=4(-1)+8
3(-1)=5(2)-13
Solution: (u,v)=(2, -1)
2. When the 2nd equation was
multiplied by -2, 4y(-2) is not=8y
3. When adding 9x+7x, it
is not=2x
3x = 6 (add equations, y’s cancel)
-1/2g =4 (add equations, h’s cancel)
x= 2
g=-8
2-y=2 (insert 2 for x in 2nd equation)
-y=0 so y=0
(solve for g)
(1/2)(-8)+h=2 (insert -8 for g in 1st equation)
-4+h=2
h=6
Check 3(2)= 6 and 2-0=2
Solution: (2, 0)
Check: (1/2)(-8)+6=2 ; -(-8)-6=2
Solution: (-8, 6)
7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44
-x-3y=-3 (multiply 1st equation by -1)
9x -3z =20
x+6y=3
-9x-18z=-6 (multiply 2nd equation by -3)
3y=0 y=0
-21z=14 z=-2/3
x+3(0)=3 (insert 0 for y in 1st equation)
9x-3(-2/3)=20 (insert -2/3 for z in 1
x=3
9x+2=20
Check: 3+3(0)=3; 3+6(0)=3
9x=18 x=2
Solution: (3,0)
Check: 9(2)-3(-2/3)=20
st
equation)
3(2)+6(-2/3)=2
Solution: (2, -2/3)
7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44
3b +2c=46
-3b-15c=-33 (multiply 2
0.1g-h=-4.3 (subtract -4.3 from both sides)
nd
equations by -3)
-13c=13 c=-1
-0.2g+h=3.6 (reorganize & multiply by -1)
-0.1g=-0.7 g=7
3b+2(-1)=46
0.1(7)-h+4.3=0 (insert 7 for g in 1st equation)
3b=48 b=16
.7-h+4.3=0
Check: 3(16)+2(-1)=46
5=h
5(-1)+16=11
Solution: (16, -1)
Check: 0.1(7)-5+4.3=0
3.6=-0.2(7)+5
Solution: (7,5)
7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44
Solve by linear combination:
4a+b=0
(reorganize 1st equation)
1a-b=5 (reorganize 2nd equation)
5a=5 a=1
1.5v-6.5w=3.5
-1.5v-6w=9 (multiply 2nd equation by -3)
-12.5w=12.5 w=-1
3(1)+9b=8b-1 (insert 1 for a in 1st equation) 0.5v+2(-1)=-3
4=-b b=-4
0.5v-2=-3
Check: 3(1)+9(-4)=8(-4)-1
0.5v=-1 v=-2
5(1)-10(-4)=4(1)-9(-4)+5
Check: 1.5(-2)-6.5(-1)=3.5
0.5(-2)+2(-1)=-3
Solution: (1,-4)
Solution: (-2,-1)
y=(9/7) x
y=-3x+12
7y=9x (multiplied 1st equation by 7)
-7y=21x-84 (multiplied 2nd equation by -7)
0=30x-84
30x=84 x=14/5
y=-3(14/5)+12= -8 2/5 +12= 3 3/5
Check: 18/5 = (9/7) (14/5)
solution: (14/5, 18/5)
18/5 = -3(14/5) + 12
45)s=speed in still air
w=wind speed
s-w =300
s+w=450
2s=750
s=375
If s=375, then 375-w=300
w=75
Check: 375-75=300
375+75=450
375mph =speed of plane
75mph =speed of wind
p414 #45-52, 56; p417 1-9
48) boat traveled upstream 8 miles in 1 hour
boat traveled downstream 8 miles in ½ hour
b-w=8
b+w=16
2b=24
b=12
w=4
boat speed-speed of water = 8 mph
boat speed +speed of water=16 mph
Boat was traveling at 12 mph,
water was going 4mph.
p414 #45-52, 56; p417 1-9
Quiz Prep
Ch 7 Systems of Linear Equations and Inequalities
November 28 A
7.1
29 A
7.2
30 H
7.3
December 1 D
7.3
2 A
Quiz 7.1-7.3
new7.4
5A
7.4
6 Penance
Service
7.5
7 Penance
Service
7.6
8 Mass
7.6 & review
9A
12 A
Chapter Review
13 A
14 H
Chapter 7 Test Review for final
15 D
Review for
final
16 A
Review for final
21 Final Exam
Ch 1-7
Due Monday
Due Tuesday
Due Wednesday
Due Thursday
Due Friday
12/5
12/6
12/7
12/8
12/9
7.4 p421 #12, 20, 28, 42, 48; chapter 1 summary p54-56
7.5 p429 #12-17,18,24,30,43-46; chapter 2 review
7.6 p435 #9-14, 26; chapter 3 review
7.6 p435 # 37,43; chapter 4 review
chapter 7 review p440 #2-32 (pick one in each section)
7.4 Applications of Linear Systems
What would you use to solve this system of equations? Why?
Cr+cp=32.75
Cp=cr+.2
Total cost regular + total cost premium =$32.75
Cost premium = cost regular + .2
Regular gas amount (cost) + premium gas amount (cost)=$32.75
10c + 15(c+.20) = 32.75
25c +3 =32.75
25c = 29.75
c=$1.19 cost for regular, $1.39 cost for premium
To check: 10(1.19) + 15(1.19+.20)=32.75
2x – y = 3
2x - 3 = y
4x + 3(2x-3) = 21
4x + 6x – 9 = 21
10x = 30
x=3
4(3) + 3y = 21
12 + 3y = 21
3y = 9
y=3
(3,3)
Check: 2(3) -3 = 3
4(3) + 3(3) = 21
-x + -2y = -2
(multiply 1st equation by -1)
x + 4y = -2
2y =-4 y = -2
x + 2(-2) = 2 x=6
(6, -2)
Check: 6 + 2(-2) = 2
6 + 4 (-2) = -2
-4{1.5x-2.5y=8.5} multiply 1st equation by -4
-6x+10y=-34
6x+30y=24 (add both equations to cancel x’s)
40y=-10
y= -.25
6x+30 (-.25)=24
6x-7.5 =24
6x =31.5
x= 5.25 ?(5.25, -.25)
Check: 1.5 (5.25)-2.5(-.25)=8.5
6(5.25)+30(-.25)=24
Solution: (5.25, -.25)
Year
Hemlock(+4)
Spruce (+6)
0
14
8
1
18
14
2
22
20
3
26
26
4
30
32
y=4x + 14
(3,26)
14
y=6x + 8
6x+8=4x+14 (substitution)
8
2x=6 x=3 (at 3 years they are equal)
y=4(3)+14=26 inches
1
2
3
4
5
Chapter 1 Summary
http://www.classzone.com/books/algebra_1/
*2 equations, same slope, different y=intercepts, no solution
*2 equations, same slope, same y=intercepts, infinite # of solutions
7.5 p429 #12-17,18,24,30,43-46; chapter 2 review
Weight of necklace = weight of 30 small beads + weight of 6 large beads
Weight of bracelet = weight of 10 small beads + weight of 2 large beads
3.6 = 30x + 6y
1.2 =10x + 2y
-3.6=-30x-6y (multiply 2nd equation by -3)
0=0
They are equivalent equations, so we cannot use them to solve the
problem.
Chapter 2 Summary
http://www.classzone.com/books/algebra_1/
7.6 p435 #9-14, 26; chapter 3 review