WELCOME TO CHAPTER 7. Objectives: 1.Solve a system of equations by graphing. 2.Solve systems from the real world. Vocabulary: system of linear equations,

WELCOME TO CHAPTER 7

Objectives:1.Solve a system of equations by

graphing.2.Solve systems from the real world.

Vocabulary: system of linear equations, solution to a system, point of intersection

Solving Linear Systems by Graphing

7.1

We have solved equations like:

We found many solutions to equations like:

Now we will find one solution to two equations like:

3(x – 4) = 5 x + 2(x – 3) = 5 – (x + 4)

2x + 4 = 12 x – 4 = 5

3x + 2y = 12 y = 2x - 5

3x + 2y = 12 y = 2x - 5

Solving Linear Systems by Graphing

7.1

Solving Linear systems by Graphing

7.1

Animalwolvescowsbeesbirdscrowsfishlions

turkeysmonkeysalligatorsequatio

ns

Grouppackherd

colonyflock

murderschoolpride

rafterstroop

congregationsystem

Solving Linear systems by Graphing

7.1

Vocabulary: system of linear equations – a group of 2 or more

equations that are linear – use a set mark { to group them.

Vocabulary: system of linear equations

x32

y

183y2x To get 1 solution, you need the same number of equations as variables.

102z3y7x

82z5yx

184z3y2x

0

2w -2x 3y 4z 18

5w x 5y 2z 8

w 7x 3y 2z 10

6w 9x-5y z

Example Solve the System by Graphing

Solve the system by graphing.

Solve a System by Graphing

1. Graph both equations.

2. Find the intersection.

3. Check the answer.

2x32

y

183y2x1 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

(3, 4)






-93y-2x

-2yx1 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

(-3, 1)







5-2xy

4yx

1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

(1, 3)







10x34

y

123y2x1 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

You Try Solve the System by Graphing






5 15

-2x y

2y x -4

51 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8







3x31

y

186y2x-

1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8


Together Real Life Linear System

You and your sister each have a savings account for college. You have $2000 and plan to deposit an additional $50 per month At the same time, your sister has a balance of $1600 and she plans to deposit $100 per month. Predict when you and your sister will have the same amount?

STANDS0_23456789

Homework Assignment:

Complete Graphing Worksheet!

7.1


substitution.2.Solve systems from the real world.

Vocabulary: none

Solving Linear Systems by Substitution

7.2

1.Solve for one of the variables and star.

2.Substitute this into the other equation.

3.Solve for the only variable.

4.Substitute this value in the star equation.

5.Clearly state your answer. Order Pair!

6.Check the answer.

How to Solve the System by Substitution

Which is the best variable to use for substitution.

Solve a System by Substitution

1. Solve for one of the variables and star.

2. Substitute this into the other equation.

3. Solve for the only variable.

4. Substitute this value in the star equation.

5. Clearly state your answer.


8y2x

9y3x-

4

335y2x

-113yx

102yx

03yx

Example Solve the System by Substitution

Solve the system by substitution.

3 3x

y

7x 2y 1Solve a System by

Substitution









6y5x

142y3xSolve a System by

Substitution









3y

5x 4y 37

x 3 Solve a System by Substitution







You Try Solve the System by Substitution


14yx

32y2x

Solve a System by Substitution









99y3x

43yxSolve a System by

Substitution









129y3x

43yx Solve a System by Substitution








In one day the Baseball Hall of Fame in Cooperstown admits 321 adults and children and collected $1590. The price of admission is $6 for an adult and $4 for a child. How many adults and how many children were admitted to the museum that day.

153 adults & 168 children

Together Real Life Linear System

MEREPEAT


Complete Substitution Worksheet!

7.2


Linear Combinations.

Vocabulary: none

Solving Linear Systems by Linear Combinations

7.3

Linear Combinations (Elimination) Method

Linear Combinations (Elimination) method is used when it appears easy to eliminate one variable from the system through transformation. Remember that linear transformations do not change the solutions of a system.

Steps

1.Put equations in STANDARD FORM.2.Multiply equations to create opposites.3.Add equations together to create one new

equation.4.Solve for the first variable.5.Substitute ^this^ variable into the top equation of

the original system.6.Solve for the second variable.7.Check your answer!

Solve the system by Linear Combinations.

Example Solve the System by LC

4x 3y 16

2x 3y 8



3x 5y 6

4x 2y 5



3x 2y 8

2y 12 5x


You Try Solve the System by LC

122y3x

22y4x



54y3x

72y3x



328y12x

123y4x


Complete Combinations Worksheet!

7.3

Objectives:1. Graph systems of linear inequalities2. Linear inequalities from real life Vocabulary: none

Solving Systems of Linear Inequalities7.6

Solve the System by Graphing


2x32

y

183y2x1 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

(3, 4)





Solve the System by Graphing


2x32

y

183y2x1 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

(3, 4)

Graph a System of Inequalities

1. Graph both inequalities.


3. Check a solution.


y 2x - 1

x 1

1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

Example 1Graph a System of Inequalities






1y

3y1 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8






1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8


1xy

2-xy






1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8


y 2 / 3x-1

y 4x 1






My first is simply a vegetable, delicious, round and green.My third and fourth are sound asleep, as plainly can be seen.My fifth is fifty, clear enough for any riddle-setter.Two of my second stacked on their sides will give my final letter.Now that my second has my parts, fit them together well.You see me now before your eyes; it's plain for all to tell.

Tonight’s Homework:Complete Graphing Inequalities Worksheet!

Algebra 1

Algebra 1 AnswerPuzzle.

My first is simply a vegetable, delicious, round and green. - Pea / P

My third and fourth are sound asleep, as plainly can be seen. - ZZ

My fifth is fifty, clear enough for any riddle-setter. - L (Roman Numeral)

Two of my second on their sides will give my final letter. - E (Take 2 U's and stack them sideways.)

Now that my second has my parts, fit them together well. - Now that YOU (u) have my parts...

You see me now before your eyes; it's plain for all to tell.

Documents

WELCOME TO CHAPTER 7. Objectives: 1.Solve a system of equations by graphing. 2.Solve systems from the real world. Vocabulary: system of linear equations,