algebra 2 lessons 3.1-3

8/14/2019 Algebra 2 Lessons 3.1-3

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Algebra 2

Systems of Equations


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What is a system of equations?

What does it mean to solve a system of

equations?


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Ways to Solve Systems of Equations

Graphing

Substitution

Elimination


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In order to solve a system of equations

graphically you typically begin by

making sure both equations are inslope-intercept form.

Wheremis the slope and bis the y-intercept.

Examples:

y = 3x- 4

y = -2x +6

Slope is 3 and y-intercept is - 4.

Slope is -2 and y-intercept is 6.

bmxy


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What information do you need to graph the

following equations?

y = 2x +1

3xy = -2

x + 2y = 4


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5

12

yx

xy


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42

1

xy

yx


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246

332

yx

yx


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62

12

1

yx

xy


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824

32

xy

yx


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1262

23

1

yx

xy


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124

34

1

yx

xy


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Lesson 3.2

Solving Systems of Equations

Algebraically


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Solving Systems of Linear Equations by Substitution

1. Solve for a variable2. Substitute for that variable in the other

equation

3. Solve this equation for the remaining variable

4. Put your solution back into either of the

original equations to solve for the other

variable

5. Check your solution with the other equation


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SPECIAL CASES

If when using substitution both variables drop out

and you get something like: 10=6

This statement is not true, so there is no solution(the lines are parallel lines)

If when using substitution both variables drop out

and you get something like: 10=10

This statement is true so there are infinite

solutions (the lines are the same lines)


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6

2

yxxy


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123

1

yx

xy


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732

52

yx

xy


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Chatty Phone charges a flat monthly fee of $20 plus 8 a minute.

Telco charges $14 plus 10 a minute. When do they charge the

same?


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WORD PROBLEMS



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Define your variables.Write your system of equations.

Solve the system of equations.


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Define your variables.

Write your system of equations.



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Two small pitchers and one large pitcher can hold 8 cups of

water. One large pitcher minus one small pitcher constitutes 2

cups of water. How many cups of water can each pitcher hold?





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A test has twenty questions worth 100 points. The test consists of

True/False questions worth 3 points each and multiple choice

questions worth 11 points each. How many multiple choice

questions are on the test?





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Bill and Steve decide to spend the afternoon at an amusement park

enjoying their favorite activities, the water slide and the gigantic

Ferris wheel. Their tickets are stamped each time they slide or

ride. At the end of the afternoon they have the following tickets:

Fun Time Amusements

Water Slide:

Ferris Wheel:

Total: $17.70

Fun Time Amusements

Water Slide:

Ferris Wheel:

Total: $15.55

Steve's TicketBill's Ticket

How much does it cost to ride the Ferris Wheel?

How much does it cost to slide on the Water Slide?


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Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts

cost $15. If she bought a total of 7 then how many of each kind did

she buy?





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There are 13 animals in the barn. Some are chickens and some are

pigs. There are 40 legs in all. How many of each animal are there?




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At Elisa's Printing Company LLC there are two kinds of printing

presses: Model A which can print 70 books per day and Model B

which can print 55 books per day. The company owns 14 total

printing presses and this allows them to print 905 books per day.How many of each type of press do they have?





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Four times one number added to another number is 36. Three

times the first number minus the other number is 20. Find the

numbers.





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One number added to three times another number is 24. Five times

the first number added to three times the other number is 36. Find

the numbers.





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Eight times a number plus five times another number is 13. The

sum of the two numbers is 1. What are the numbers?




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A library contains 2000 books. There are 3 times as many non-

fiction books as fiction books. Write and solve a system of

equations to determine the number of nonfiction and fiction

books.





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How do the quarter Pounder and Whopper with cheese measure up

in the calorie department? Actually, not too well. Two Quarter

Pounders and three Whoppers with cheese provide 2607 calories.

Even one of each provide enough calories to bring tears to JennyCraigs eyes-9 calories in excess of what is allowed on a 1000

calories-a day diet. Find the calories in each item.


Write your system of equations.Solve the system of equations.


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Solving Systems of Linear Equations by Elimination

1. Write equations in standard form (variables line up)2. Multiply one of the equations to get coefficients of

one of the variables to be opposites

3. Add (or subtract) equationsso that one variable

drops out4. Solve for the remaining variable.

5. Plug you solution back into one of the originalequations and solve for the other variable.

62


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43

62

yx

yx


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3

53

yx

yx


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52

43

yx

xy


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432


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94

432

yx

yx


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532


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425

532

yx

yx


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Applications


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3.2 Applications of Linear

Systems of Equations1. Determine what you are to findassign variables

2. Draw a diagram, figure or make a chart of

information.3. Write the system of equations

4. Solve the system using substitution or elimination

5. Answer the question from the problem.


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algebra 2 lessons 3.1-3

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