Linear Systems

Chapter 7 Review Game• 7.1 Solving by Graphing• 7.2 Solving by Substitution• 7.3 & 7.4 Solving by Elimination• 7.5 Special Systems

Game Board

TargetHome Depot

LowesWal-Mart

10 10 10 10

20 20 20 20

30 30 30 30

40 40 40 40

50 50 50 50

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Target for 10pts

When graphing a system of equations describe how you find your answer.

Target for 10pts Ans

1. Solve equations for y2. Graph the equations3. Look for intersection point

(x,y)

When graphing a system of equations describe how you find your answer.

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Target for 20ptsIs (2, -3) the solution to this system? Explain.

63

5

yx

yx

Target for 20pts AnsIs (2, -3) the solution to this

system? Explain.

55

532

5)3(2

5

yx

63

5

yx

yx

63

636

63)2(3

63

yx

NO! (2,-3) only works in one equation. To be a solution it must work in ALL equations in the system

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Target for 30ptsSolve this system by graphing

105

5

xy

xy

Target for 30pts AnsSolve this system by

graphing

105

5

xy

xy  

 

(1, 5)

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Target for 40ptsSolve this system by graphing

62

2

yx

yx

Target for 40pts AnsSolve this system by

graphing

 

 

(4, 2)

62

2

yx

yx

62

2

xy

xy

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Target for 50ptsSolve this system by graphing

3034

335

yx

yx

Target for 50pts AnsSolve this system by

graphing

 

 

(3, 6)

103

4

13

5

xy

xy

3034

335

yx

yx

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Home Depot for 10ptsWhen solving this system by substitution, which variable would you isolate and why? 

Home Depot for 10pts AnsWhen solving this system by substitution,

which variable would you isolate and why? 

Solve for the first y because it has a coefficient of 1 (easiest to get by itself)

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Home Depot for 20ptsSolve by Substitution

 

Home Depot for 20pts Ans

Solve by Substitution 

 

 

(1,7)

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Home Depot for 30ptsSolve by Substitution

 

Home Depot for 30pts Ans

Solve by Substitution 

 

 

 

(5,-8)

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Home Depot for 40ptsSolve by Substitution

 

Home Depot for 40pts Ans

Solve by Substitution

 

(4,3) 

 

 

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Home Depot for 50ptsMrs. Brown bought one bag of grass seed and 3 jugs of fertilizer for her yard and paid a total of $30.82.

Mrs. Laurenzi needed 4 bags of grass seed and 2 jugs of fertilizer and paid a total of $60.48.

Find the cost of a bag of grass seed and a jug of fertilizer.

x – cost of grass seed

y – cost of fertilizer

Mrs. Brown bought one bag of grass seed and 3 jugs of fertilizer for her yard and paid a total of $30.82. Mrs. Laurenzi needed 4 bags of grass seed and 2 jugs of fertilizer and paid a total of $60.48. Find the cost of a bag of grass seed and a jug of fertilizer.

Home Depot for 50pts Ans

$11.98 for Grass

$6.28 for Fertilizer

 

 

 

x – cost of grass seed y – cost of fertilizer

48.6024

82.303

yx

yx

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Lowes for 10pts

What do we want to have happen when you use the elimination method?

Lowes for 10pts Ans

What do we want to have happen when you use the elimination method?

We want one variable to cancel out so we can solve for the leftover variable.

156

3668

xy

xyEx: The x’s cancel and we can solve for y

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Lowes for 20pts

Solve the system by Elimination

174

29

yx

yx

Lowes for 20pts Ans

Solve the system by Elimination

174

29

yx

yx

3

155

x

x29

227

2)3(9

29

y

y

y

yx

(-3,29)

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Lowes for 30pts

Solve the system by Elimination

3643

282011

yx

yx

Lowes for 30pts Ans

Solve the system by Elimination

3643

282011

yx

yx

8

20826

x

x

3

124

36424

364)8(3

3643

y

y

y

y

yx

(8,3)

5( )

1802015

282011

yx

yx

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Lowes for 40pts

Solve the system by Elimination

38521237

yxyx

Lowes for 40pts Ans

3852

1237

yx

yxSolve the system by Elimination

10

29029

y

y

6

122

38502

38)10(52

3852

x

x

x

x

yx

(-6,10)

7( )

2663514

24614

yx

yx-2( )

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Lowes for 50ptsMr. Laurenzi and Mr. Brown order the same fencing online. Mr. L gets 7 sections of fencing and pays a shipping fee for a total of $177.72. Mr. B gets 11 sections plus the same shipping fee for a total of $274.56. What is the cost of one section of fence and the shipping fee?

x – cost per fence

y – cost of shipping

Lowes for 50pts Ans

56.2741172.1777

yxyx

21.24

84.964

x

x

25.8

72.17747.169

72.177)21.24(7

72.1777

y

y

y

yx

$24.21 for each Fence$8.25 for Shipping

-1( )

56.27411

72.1777

yx

yx

Mr. Laurenzi and Mr. Brown order the same fencing online. Mr. L gets 7 sections of fencing and pays a shipping fee for a total of $177.72. Mr. B gets 11 sections plus the same shipping fee for a total of $274.56. What is the cost of one section of fence and the shipping fee?x – cost per fence y – cost of shipping

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Wal-Mart for 10pts

Describe the 3 possibilities for a system of 2 linear equations.

(What could the graph of the 2 lines look like?)

Wal-Mart for 10pts Ans

Describe the 3 possibilities for a system of 2 linear equations. (What could the graph of the 2 lines look like?)

One Solution-Lines cross

No Solutions-Parallel lines

Infinitely Many Solutions-Overlapping lines

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Wal-Mart for 20ptsTell whether the system has one, none, or infinitely many solutions. Explain how you know.

233

4

yx

yx

Wal-Mart for 20pts AnsTell whether the system has one, none, or infinitely many

solutions. Explain how you know.

233

4

yx

yx

100 4yx

NO SOLUTIONS!

3( )

233

1233

yx

yx

FALSE!

Elimination Method:

Substitution Method:

212

23123

23)4(3

yy

yy

FALSE!

Solve for y (compare m & b):

3

2

4

xy

xySame m,

diff b

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Wal-Mart for 30ptsTell whether the system has one, none, or infinitely many solutions. Explain how you know.

262

13

yx

yx

Wal-Mart for 30pts Ans

262

13

yx

yx

0013 yx

INFINITELY MANY SOLUTIONS!

2( )

262

262

yx

yx

Tell whether the system has one, none, or infinitely many solutions. Explain how you know.

TRUE!

Elimination Method:

Substitution Method:

22

2626

26)13(2

yy

yy

TRUE!

Solve for y (compare m & b):

3

1

3

13

1

3

1

xy

xy Same m, same b

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Wal-Mart for 40ptsExplain how you would determine the number of solutions for this system without using substitution or elimination.

6212

26yx

xy

Wal-Mart for 40pts AnsExplain how you would determine the number of solutions for this

system without using substitution or elimination.

NO SOLUTIONS!

Solve for y (compare m & b):

Same SlopesDiff y-int

621226

yx

xy 26 xy

166122

xyxy

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Wal-Mart for 50ptsTell whether the system has one, none, or infinitely many solutions. Explain how you know.

6250yx

yx

Wal-Mart for 50pts AnsTell whether the system has one, none, or infinitely many

solutions. Explain how you know.

6250yx

yx

263

xx

0yx

ONE SOLUTION!

-5( )

625055

yxyx

One Variable

Left!

Elimination Method:

Substitution Method:

26362)(5

yyyy

Solve for y (compare m & b):

5

6

2

5

xy

xy

Diff Slopes!

One Variable

Left!

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