tuesday, 2/9/10 swbat… solve systems of equations using the graphing method

Tuesday, 2/9/10

SWBAT… solve systems of equations using the graphing methodAgenda1. WU (5 min)2. Activity – Systems of equations: graphing method (20 min)3. Presentations (15 min)4. Conclusions (10 min)

Warm-Up:1. Write hw in planner2. Read the graphing/ substitution/ elimination examples3. Questions from back of agenda problems?

HW#1: Graphing method

Systems of Equations: Graphing Method

What are systems of equations? A collection of equations involving the same

set of variables. We will be dealing with two equations and two

variables.

Activity-Systems of equations: Graphing

I have given one person a note card with a system of equations

You are to work with a person who has a note card 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.)

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

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

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.

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

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 23

3

x

yStep 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 23

3

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 33 9 9

.

x yx y

2 35

4

5 3

. y x

y x

3 32 6

. x yx y

x

yThe two equations in slope-intercept form are:

y x

y x or y x

13

1

39

99

13

1

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 .

The two equations in slope-intercept form are:

x

y

y x

y x

35

4

35

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 xy x

32 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).

Wed, 2/10/10

SWBAT… solve systems of equations using the substitution methodAgenda1. WU (5 min)2. Examples – Systems of equations: substitution method

Warm-Up:1. Write hw in planner2. Describe the advantages and disadvantages to solving systems of equations by graphing.

HW#2: Substitution method HW#3: Elimination method

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

Set up a systems of equations(substitution method)

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

Tues, 2/16/10

SWBAT… solve systems of equations using the elimination methodAgenda1. WU (10 min)2. 3 Examples – Systems of equations: elimination method (15 min)3. Work on hw#1, 2, or 3 (20 min)4. Turn in hw#1/2

WU: Use the substitution to solve the system of equations

y = 2x – 4 x = y – 1 -6x + 3y = -12 -x + y = -1

HW#3: Elimination method

Elimination using AdditionUse the elimination method to solve the system of equations:

-3x + 5y = -11 3x + 7y = -1

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.

Elimination using Subtraction

Use the elimination method to solve the system of equations:

2t + 5r = 6 9r + 2t = 22

Elimination using Multiplication

Use the elimination method to solve the system of equations:

5x + 6y = -8 2x + 3y = -5

Wed, 2/17/10

SWBAT… apply systems of equations Agenda1. WU (5 min)2. Concept Summary – Solving Systems of Equations (15 min)3. Real-life systems examples

Warm-Up:1. Write hw in planner2. Questions from hw #3-elimination?

HW#4: Real-life systems of equations

Fill in the chart below:

Method The Best Time to UseGraphingSubstitutionElimination using Addition




Method The Best Time to UseGraphing To estimate solutions, since graphing usually

does not give an exact solution.

Substitution

Elimination using AdditionElimination using Subtraction





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

Elimination using AdditionElimination using Subtraction






Elimination using Addition

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.

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 manager uses systems of equations to plan employee time

The local bakery is making chocolate chip cookies and bread. Each batch of cookies take 20 minutes to prepare and 10 minutes to bake. Each loaf of bread takes 10 minutes to prepare and 30 minutes to bake. The bakery’s management has allotted 800 minutes of employee time (preparation) and 900 minutes of oven time (baking). How many of each should be baked?

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?

tuesday, 2/9/10 swbat… solve systems of equations using the graphing method

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