6.1 Solving One-Step Linear Inequalities x + 8 > 1

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 VariablesGraph 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 InequalitiesNovember 28 A7.1

29 A7.2

30 H7.3

December 1 D7.3

2 AQuiz 7.1-7.3

new7.4

5 A7.4

6 Penance Service

7.5

7 Penance Service

7.6

8 Mass7.6 & review

9 A

12 AChapter Review

13 A Chapter 7

Test

14 HReview for final

15 DReview for

final

16 AReview for final

21 Final Exam Ch 1-7

Due Tuesday 11/29 7.1 p401 12,16,18, 22,26,36,44Due Wednesday 11/30 7.2 p408-411 #14,16,18,20, 26, 30,35,44,48-51Due Thursday 12/1 7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44Due Friday 12/2 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

2(5x)-2(4y) = 2(3) (multiply first equation by 2 to get y’s to cancel)

10x -8y =62x + 8y = -212x = 4x= 1/3

To find y: 2(1/3)+8y= -22/3 +8y = -28y=-2 2/38y= -8/3y=-1/3

Check: 5(1/3) -4(-1/3) = 3 2(1/3) +8(-1/3)= -2

Solution: (1/3, -1/3)

Solve by linear combination:3x-6y= -12 -x+3y=6

3x -6y= -12-3x+9y= 18 (multiply each term by 3)

3y=6 y=2

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 (to find “u”, plug in v=-1 into one of the equations)2u=4u=2

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

7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44

3x = 6 (add equations, y’s cancel)

x= 2

2-y=2 (insert 2 for x in 2nd equation)

-y=0 so y=0

Check 3(2)= 6 and 2-0=2

Solution: (2, 0)

-1/2g =4 (add equations, h’s cancel)

g=-8 (solve for g)

(1/2)(-8)+h=2 (insert -8 for g in 1st equation)

-4+h=2

h=6

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)

x+6y=3

3y=0 y=0

x+3(0)=3 (insert 0 for y in 1st equation)

x=3

Check: 3+3(0)=3; 3+6(0)=3

Solution: (3,0)

9x -3z =20

-9x-18z=-6 (multiply 2nd equation by -3)

-21z=14 z=-2/3

9x-3(-2/3)=20 (insert -2/3 for z in 1st equation)

9x+2=20

9x=18 x=2

Check: 9(2)-3(-2/3)=20

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 2nd equations by -3)

-13c=13 c=-1

3b+2(-1)=46

3b=48 b=16

Check: 3(16)+2(-1)=46

5(-1)+16=11

Solution: (16, -1)

0.1g-h=-4.3 (subtract -4.3 from both sides)

-0.2g+h=3.6 (reorganize & multiply by -1)

-0.1g=-0.7 g=7

0.1(7)-h+4.3=0 (insert 7 for g in 1st equation)

.7-h+4.3=0

5=h

Check: 0.1(7)-5+4.3=0

3.6=-0.2(7)+5

Solution: (7,5)

Solve by linear combination:

4a+b=0 (reorganize 1st equation)

1a-b=5 (reorganize 2nd equation)

5a=5 a=1

3(1)+9b=8b-1 (insert 1 for a in 1st equation)

4=-b b=-4

Check: 3(1)+9(-4)=8(-4)-1

5(1)-10(-4)=4(1)-9(-4)+5

Solution: (1,-4)

1.5v-6.5w=3.5

-1.5v-6w=9 (multiply 2nd equation by -3)

-12.5w=12.5 w=-1

0.5v+2(-1)=-3

0.5v-2=-3

0.5v=-1 v=-2

Check: 1.5(-2)-6.5(-1)=3.5

0.5(-2)+2(-1)=-3

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 solution: (14/5, 18/5)

Check: 18/5 = (9/7) (14/5) 18/5 = -3(14/5) + 12

p414 #45-52, 56; p417 1-9

45)s=speed in still air w=wind speed

s-w =300s+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 boat speed-speed of water = 8 mph b+w=16 boat speed +speed of water=16 mph 2b=24 b=12 w=4

Boat was traveling at 12 mph, water was going 4mph.

Quiz Prep

Ch 7 Systems of Linear Equations and InequalitiesNovember 28 A7.1

29 A7.2

30 H7.3

December 1 D7.3

2 AQuiz 7.1-7.3

new7.4

5 A7.4

6 Penance Service

7.5

7 Penance Service

7.6

8 Mass7.6 & review

9 A

12 AChapter Review

13 A Chapter 7

Test

14 HReview for final

15 DReview for

final

16 AReview for final

21 Final Exam Ch 1-7

 Due Monday 12/5 7.4 p421 #12, 20, 28, 42, 48; chapter 1 summary p54-56Due Tuesday 12/6 7.5 p429 #12-17,18,24,30,43-46; chapter 2 reviewDue Wednesday 12/7 7.6 p435 #9-14, 26; chapter 3 reviewDue Thursday 12/8 7.6 p435 # 37,43; chapter 4 reviewDue Friday 12/9 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?

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

Cr+cp=32.75

Cp=cr+.2

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)

y=4x + 14

y=6x + 8

6x+8=4x+14 (substitution)

2x=6 x=3 (at 3 years they are equal)

y=4(3)+14=26 inches

Year

Hemlock(+4)

Spruce (+6)

0 14 8

1 18 14

2 22 20

3 26 26

4 30 3214

8

1 2 3 4 5

(3,26)

y=6x

+8

y=4x+

1

4

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