WELCOME TO CHAPTER 7. Objectives: 1.Solve a system of equations by graphing. 2.Solve systems from...

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

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

Solving Linear Systems by Graphing

Solving Linear systems by Graphing

Animalwolvescowsbeesbirdscrowsfishlions

turkeysmonkeysalligatorsequatio

Grouppackherd

colonyflock

murderschoolpride

rafterstroop

congregationsystem

Solving Linear systems by Graphing

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

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

102z3y7x

82z5yx

184z3y2x

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.

183y2x1 2 3 4 5 6 7 8 9 1

-6-4 -2-8

(3, 4)

-93y-2x

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

-6-4 -2-8

(-3, 1)

1 2 3 4 5 6 7 8 9 10

-6-4 -2-8

(1, 3)

123y2x1 2 3 4 5 6 7 8 9 1

-6-4 -2-8

You Try Solve the System by Graphing

2y x -4

51 2 3 4 5 6 7 8 9 1

-6-4 -2-8

186y2x-

1 2 3 4 5 6 7 8 9 10

-6-4 -2-8

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!

substitution.2.Solve systems from the real world.

Vocabulary: none

Solving Linear Systems 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. 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.

335y2x

-113yx

Example Solve the System by Substitution

Solve the system by substitution.

7x 2y 1Solve a System by

Substitution

142y3xSolve a System by

Substitution

5x 4y 37

x 3 Solve a System by Substitution

You Try Solve the System by Substitution

Solve a System by Substitution

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!

Linear Combinations.

Vocabulary: none

Solving Linear Systems by Linear Combinations

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.

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

328y12x

123y4x

Complete Combinations Worksheet!

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

183y2x1 2 3 4 5 6 7 8 9 1

-6-4 -2-8

(3, 4)

Solve the System by Graphing

183y2x1 2 3 4 5 6 7 8 9 1

-6-4 -2-8

(3, 4)

Graph a System of Inequalities

1. Graph both inequalities.

3. Check a solution.

y 2x - 1

1 2 3 4 5 6 7 8 9 10

-6-4 -2-8

Example 1Graph a System of Inequalities

3y1 2 3 4 5 6 7 8 9 1

-6-4 -2-8

1 2 3 4 5 6 7 8 9 10

-6-4 -2-8

1 2 3 4 5 6 7 8 9 10

-6-4 -2-8

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.

WELCOME TO CHAPTER 7. Objectives: 1.Solve a system of equations by graphing. 2.Solve systems from...

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