monday, 1/24tuesday, 1/25wednesday, 1/26thursday, 1/27friday, 1/28 final corrections systems of...
TRANSCRIPT
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
Monday, 1/31 Tuesday, 2/1 Wednesday, 2/2 Thursday, 2/3 Friday, 2/4
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
Monday, 2/7 Tuesday, 2/8 Wednesday, 2/9 Thursday, 2/10 Friday, 2/11
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
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
Monday, 1/31 Tuesday, 2/1 Wednesday, 2/2 Thursday, 2/3 Friday, 2/4
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
Monday, 2/7 Tuesday, 2/8 Wednesday, 2/9 Thursday, 2/10 Friday, 2/11
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
Different m values(b can be same or different)
One
None
Infinite
Conclusions
Compare m and b
Number of Solutions
Different m values(b can be same or different)
One
Same m value, but different b values
None
Infinite
Conclusions
Compare m and b
Number of Solutions
Different m values(b can be same or different)
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
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
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%
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
Elimination using Multiplication
Fill in the chart below:
Method The Best Time to Use
Graphing To estimate solutions, since graphing usually does not give an exact solution.
Substitution
Elimination using Addition
Elimination using Subtraction
Elimination using Multiplication
Fill in the chart below:
Method The Best Time to Use
Graphing To estimate solutions, since graphing usually does not give an exact solution.
Substitution If one of the variables in either equation has a coefficient of 1 or -1.
Elimination using Addition
Elimination using Subtraction
Elimination using Multiplication
Fill in the chart below:
Method The Best Time to Use
Graphing To estimate solutions, since graphing usually does not give an exact solution.
Substitution If one of the variables in either equation has a coefficient of 1 or -1.
Elimination using Addition
If one of the variables has opposite coefficients in the two equations.
Elimination using Subtraction
Elimination using Multiplication
Fill in the chart below:
Method The Best Time to Use
Graphing To estimate solutions, since graphing usually does not give an exact solution.
Substitution If one of the variables in either equation has a coefficient of 1 or -1.
Elimination using Addition
If one of the variables has opposite coefficients in the two equations.
Elimination using Subtraction
If one of the variables has the same coefficient in the two equations.
Elimination using Multiplication
Fill in the chart below:
Method The Best Time to Use
Graphing To estimate solutions, since graphing usually does not give an exact solution.
Substitution If one of the variables in either equation has a coefficient of 1 or -1.
Elimination using Addition
If one of the variables has opposite coefficients in the two equations.
Elimination using Subtraction
If one of the variables has the same coefficient in the two equations.
Elimination using Multiplication
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?