Monday, 1/24Tuesday, 1/25Wednesday, 1/26Thursday, 1/27Friday, 1/28 Final corrections Systems of equations: graphing No classes – End of S1 Monday, 1/31Tuesday,

Monday, 1/24 Tuesday, 1/25 Wednesday, 1/26 Thursday, 1/27 Friday, 1/28

Final corrections

Systems of

equations:

graphing

No classes – End of S1


Systems of

equations:

substitution

EXPLORE Testing

Work KeysTesting

Report Card Pick-Up 4PM –6PM (EC)

Systems of

equations:

Elimination

using addition/

subtraction

Systems of

equations:

elimination

using

multiplication


Quiz:

Systems of

Equations

Review

for test

Review

for test

Test:

Systems of

equations

No classes – Staff Dev Day

Valentines Dance: 7PM – 11PM

Step 1) Write the equations of the lines in slope-intercept form.

Step 2) Graph each line on the same graph.

Step 3) Determine the point of intersection and write this point as an ordered pair.

• If the two equations represent the same line, the system of equations has infinitely many solutions (same line.)

• If the two equations have no points in common, the system of equations has no solution (parallel lines.)

Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution.

x – y = 2

3y + 2x = 9Step 1: Write each equation in slope-intercept form.

x – y = 2

+ y +y

x = 2 + y

- 2 -2

x – 2 = y

3y + 2x = 9

- 2x -2x3y = -2x + 93 3 3

y x 2

33

x

y

Step 2: Graph each line on the same graph

Step 3: Determine the point of intersection.

The point of intersection of the two lines is the point (3,1).

This system of equations has one solution, the point (3,1) .

y = x – 2

y x 2

33

Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution.

1 3 3

3 9 9

.

x y

x y

23

54

5 3

. y x

y x

3 3

2 6

. x y

x y

x

yThe two equations in slope-intercept form are:y x

y x

3

2 6

Plot points for each line.

Draw in the lines.

This system of equations represents two intersecting lines.

The solution to this system of equations is a single point (3,0).

The two equations in slope-intercept form are:

x

y

y x

y x

3

54

3

5

Plot points for each line.

Draw in the lines.

This system of equations represents two parallel lines.

This system of equations has no solution because these two lines have no points in common.

x

yThe two equations in slope-intercept form are:

y x

y x o r y x

1

31

3

9

9

9

1

31

Plot points for each line.Draw in the lines.

These two equations represent the same line.

Therefore, this system of equations has infinitely many solutions .

Conclusions

The solution to a systems of equations is the point where the two lines intersect (one solution)

No solution will be parallel lines Infinite solution will be the same line

Activity-Systems of equations: Graphing

Each pair has a note card with a system of equations Working in pairs: Directions: Graph the system of equations on a

big piece of graph paper. Determine whether the system has one solution, no solution, or infinite solutions. If the system has one solution, name it (see worksheet on how to name it.)

This will be our first project grade. Show your work on your graph paper (don’t write on

the note card) After 20 minutes, I will randomly choose 3 groups to

present their system

Mon, 1/31

SWBAT… solve systems of equations using the substitution methodAgenda

1. WU (10 min)

2. Announcements (5 min)

3. Examples – Systems of equations: substitution method

Warm-Up:

1. Describe the advantages and disadvantages to solving systems of equations by graphing.

2.

Compare m and b(same or different)

Number of Solutions

One

None

Infinite


Final corrections

Systems of

equations:

graphing

No classes – End of S1


Systems of

equations:

substitution

EXPLORE Testing (8:45-12)

Adv 406: Rm 206Adv 407: Rm 208Adv 408: Rm 201Adv 409: Mac Lab

WorkKeysTesting (8:45-12)

Report Card Pick-Up 4PM–6PM

(EC)

Systems of

equations:

Elimination

using addition/

subtraction

Systems of

equations:

elimination

using

multiplication


Quiz:

Systems of

Equations

Review

for test

Review

for test

Test:

Systems of

equations

No classes – Staff Dev Day

Valentines Dance: 7PM – 11PM

Tuesday’s & Wednesday’s testing rooms

Announcements Welcome to Quarter 3, Semester 2!!! All students start this new semester with 100% (A+).

Your job is to keep it!! Everyone has been given 100 work ethic points. For the second semester:

Each tardy will result in a deduction of 10 points. Not having your planner will result in a deduction of 10

points. Not wearing your ID or Infinity polo will result in a

deduction of 10 points each. Wearing hats, hoodies, jackets, fleeces, or ear buds will

result in a deduction of 10 points each, will be confiscated, and will not be returned until the end of the day. (These items apply in the hallways, cafeteria, advisories also – not just in class)

2nd Period Semester 1 Grades

12

14

5

2

00

2

4

6

8

10

12

14

16

A B C D F

Grade

Nu

mb

er o

f S

tud

ents

Mean: 86%Range: 60% - 99.9%

Conclusions

Compare m and b

Number of Solutions

One

None

Infinite

Conclusions

Compare m and b

Number of Solutions

Different m values(b can be same or different)

One

None

Infinite

Conclusions

Compare m and b

Number of Solutions


One

Same m value, but different b values

None

Infinite

Conclusions

Compare m and b

Number of Solutions


One

Same m value, but different b values

None

Same m value and same b value

Infinite

HW#1: Systems-Graphing Method Answers:

1. 1 Solution: (1, 2)

2. 1 Solution: (-4, -2)

3. Infinite Solutions

4. 1 Solution: (-2, -2)

5. 1 Solution: (-3, 5)

6. Infinite Solutions

7. Infinite Solutions 1. Top equation: multiply by 5/8

2. Bottom equation: multiply by 5/2

8. 1 Solution: (3, -3)1. Top equation: multiply by 3/2

2. Bottom equation: multiply by 5/1

Systems of equations: substitution method

Example 1: Solve the system using substitution

The sum of two numbers is 20. The difference between three times the larger number and twice the smaller is 40.

Follow the directions from the box and solve the above system.

The steps to solving systems of equations using the substitution method are shown in the box on

HW#2

How can you verify that your solution is correct? x + y = 20

3x – 2y = 40

Answer: (4, 16)

Example 2: Solve the system using substitution

3x = 3y + 3

x – y = 1

HW#2: Substitution Answers

1. (5, 10)2. (0, 2)3. (2, 0)4. No Solution5. Infinite Solution6. (0, -6)7. a.) t = cost of a taco, b = cost of a burrito8. b.) 3t + 2b = 7.40

4t + 1b = 6.459. c.) c = 1.1, b = 2.0510. d.) The cost of 2 tacos is $2.20 and the cost of

2 burritos is $4.10.

Thurs, 2/27

SWBAT… solve systems of equations using the elimination methodAgenda

1. WU (10 min)

2. Review hw (10 min)

3. 3 Examples – Systems of equations: elimination method (15 min)

WU: Use substitution to solve the system of equations

1.) y = 2x – 4 2.) x = y – 1

-6x + 3y = -12 -x + y = -1

HW#3: Elimination method

Ex.1: Elimination using Addition

Negative three times one number plus five times another number is -11.

Three times the first number plus 7 times the other number is -1.

Find the numbers.

-3x + 5y = -11

3x + 7y = -1

Ex. 2: Elimination using Subtraction

2t + 5r = 6

9r + 2t = 22

Mon, 1/31

SWBAT… solve systems of equations using elimination using multiplication Agenda

1. WU (10 min)

2. One example: elimination using multiplication (10 min)

3. Review hw#3: elimination (10 min)

4. Concept Summary – Solving Systems of Equations (15 min)

WU: Solve using elimination using multiplication: 1. 5x + 6y = -8

2x + 3y = -5

2. Verify that your solution is correct.HW#4: Systems of Equations: Real-life

and HW#5: Systems of Equations – MC

Announcements Welcome to Quarter 3, Semester 2!!! All students start this new semester with 100% (A+).

Your job is to keep it!! Everyone has been given 200 work ethic points. For the second semester:

Each tardy will result in a deduction of 25 points.

1st Period Semester 1 Grades

12 12

4

1 1

0

2

4

6

8

10

12

14

A B C D F

Grade

Nu

mb

er o

f S

tud

ents

Mean: 86%Range: 57% - 99%

Elimination using Multiplication

9x + 5y = 34

8x – 2y = -2

HW#3: Elimination Answers1. (5, 2)2. (1, 6)3. (6, 1)4. (-3, 5)5. (4, -1)6. (2, 3)7. (2, -3)8. (1, 2)9. x = 6, y = 1810. c = 3.95, a = 5.9511. a.) (4, 1)12. d.) (0, 3) (2, 5)

Fill in the chart below:

Method The Best Time to Use

Graphing

Substitution

Elimination using Addition

Elimination using Subtraction




Graphing To estimate solutions, since graphing usually does not give an exact solution.

Substitution







Substitution If one of the variables in either equation has a coefficient of 1 or -1.









If one of the variables has opposite coefficients in the two equations.










If one of the variables has the same coefficient in the two equations.









If one of the variables has the same coefficient in the two equations.


If none of the coefficients are 1 or -1 and neither of the variables can be eliminated by simply adding or subtracting the equations.

Which method is best to use? Why?

1. x = 12y – 143y + 2x = -2

Substitution; one equation is solved for x

2. 20x + 3y = 20-20x + 5y = 60

Elimination; add to eliminate x

3. y = x + 2y = -2x + 3

Substitution; both equations are solved for y

HOMEWORK:

HW#1 – HW#5 will be collected on Friday.

Quiz on systems on Friday.

Extra Credit:

Find a value of n such that the x-value of the solution of the system below is 4. Show or explain your work.

5x – 10y = 50

nx + 10y = 6

How a customer uses systems of equations to see what he paid

Two groups of students order burritos and tacos at Atontonilco. One order of 3 burritos and 4 tacos costs $11.33. The other order of 9 burritos and 5 tacos costs $23.56. How much did each taco and burrito cost?

How a fair manager uses systems of equations to plan his inventory

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. How many children and how many adults attended?

How a customer uses systems of equations to see what he paid

A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?

Documents

Monday, 1/24Tuesday, 1/25Wednesday, 1/26Thursday, 1/27Friday, 1/28 Final corrections Systems of equations: graphing No classes – End of S1 Monday, 1/31Tuesday,