Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213

Linear System of Equations• Classify Systems• Independent• Dependent• Inconsistent

Methods for Solving• Tables• Graphing• Substitution• Elimination• Matrices

-5 5

-5

5

x

y

{𝑦=𝑥+3𝑥+𝑦=1

−2 1 3

−1 2 2

0 3 1[−𝟏 𝟏𝟏 𝟏

∨𝟑𝟏 ] [𝟏 𝟎

𝟎 𝟏|−𝟏𝟐 ]

(−1 ,2)

Linear System of Inequalities

{−𝒙+𝟐 𝒚 ≤𝟒𝒙+𝒚<𝟖𝒙 ≥𝟐𝒚 ≥𝟏

-1 10-1

10

x

y

-1 10-1

10

x

y

-1 10-1

10

x

y

x

y

x

yMaximize:

Pg. 187 #1 – 13

Linear SystemsClassifying

Systems

Solving 2 Variable Systems

Solving 3 Variable Systems

Inequalities Modeling(Application)

10 10 10 10 10

20 20 20 20 20

30 30 30 30 30

40 40 40 40 40

50 50 50 50 50

Answer

Without graphing, classify each system. (independent, dependent, inconsistent)

{ 5𝑥+3 𝑦=9

𝑦=− 35𝑥+3


{ 5𝑥+3 𝑦=9

𝑦=− 35𝑥+3

Independent

Answer


{12𝑥−4 𝑦=20𝑦=3𝑥+3


{12𝑥−4 𝑦=20𝑦=3𝑥+3

Inconsistent

Answer


{2𝑥+6 𝑦=12

𝑦=− 13𝑥+2


{2𝑥+6 𝑦=12

𝑦=− 13𝑥+2

Dependent

Answer


{−12 𝑥+2 𝑦=−1518 𝑥−3 𝑦=27


{−12 𝑥+2 𝑦=−1518 𝑥−3 𝑦=27

Inconsistent

Answer


{15 𝑥+6 𝑦=610 𝑥+4 𝑦=4


{15 𝑥+6 𝑦=610 𝑥+4 𝑦=4

Dependent

-5 5

-5

5

x

y

Answer

Solve the system by: Graphing

{ 𝑦=2 𝑥−4𝑥−4 𝑦=−3

Solve the system by: Graphing

{ 𝑦=2 𝑥−4𝑥−4 𝑦=−12

-5 5

-5

5

x

y

(4 , 4)

Answer

Solve the system by: Substitution

{−2 𝑥− 𝑦=−9𝑦=−5 𝑥+15

Solve the system by: Substitution

{−2 𝑥− 𝑦=−9𝑦=−5 𝑥+15

(2 ,5)

Answer

Solve the system by: Elimination

{−8 𝑥−7 𝑦=−285 𝑥+6 𝑦=24

Solve the system by: Elimination

{−8 𝑥−7 𝑦=−285 𝑥+6 𝑦=24

(0 ,4)

Answer

Solve the system by: Your Choice

{6 𝑦+11+𝑥=08 𝑥=−4−6 𝑦


{6 𝑦+11+𝑥=08 𝑥=−4−6 𝑦

(1 ,−2)

Answer


{ −4 𝑦=8 𝑥+120=18 𝑦+12𝑥−90


{ −4 𝑦=8 𝑥+120=18 𝑦+12𝑥−90

(−6 ,9)

Answer

Write a matrix to represent the system.

{ 6 𝑥+2 𝑦+𝑧=30−3𝑥+3 𝑧=0

−2 𝑥+5 𝑦+4 𝑧=3

Write a matrix to represent the system.

{ 6 𝑥+2 𝑦+𝑧=30−3𝑥+3 𝑧=0

−2 𝑥+5 𝑦+4 𝑧=3

[ 6 2 1−3 0 3−2 5 4|

3 003 ]

Answer

What system is represented by the matrix:

[2 7 13 −2 01 2 1|

960 ]

What system is represented by the matrix:

{2𝑥+7 𝑦+𝑧=93 𝑥−2 𝑦=6𝑥+2 𝑦+𝑧=0

[2 7 13 −2 01 2 1|

960 ]

Answer


{ 6 𝑥−5 𝑧=−11𝑥− 𝑦=−12

−4 𝑥−4 𝑦+5 𝑧=−25


{ 6 𝑥−5 𝑧=−11𝑥− 𝑦=−12

−4 𝑥−4 𝑦+5 𝑧=−25

[ 6 0 −51 −1 0−4 −4 5 |−11

−12−25 ] (−6 ,6 ,−5)

Answer


{6 𝑥−5 𝑦+𝑧=−172 𝑥− 𝑦+𝑧=−5𝑧=−3𝑥−8


{6 𝑥−5 𝑦+𝑧=−172 𝑥− 𝑦+𝑧=−5𝑧=−3𝑥−8

[6 −5 12 −1 13 0 1|

−17−5−8 ]

(3 ,0 ,1)

Answer


{ 𝑥+6 𝑦−2 𝑧=25𝑥−5 𝑦−3 𝑧=9

6 𝑥+ 𝑦+6 𝑧=−28

Solve the system

{ 𝑥+6 𝑦−2 𝑧=25𝑥−5 𝑦−3 𝑧=9

6 𝑥+ 𝑦+6 𝑧=−28

[1 6 −21 −5 −36 1 6 | 25

9−28 ] (1 ,2 ,−6)

-5 5

-5

5

x

y

Answer

Graph the solution to each inequality

7 𝑥−3 𝑦>−9

-5 5

-5

5

x

y


7 𝑥−3 𝑦>−9

-5 5

-5

5

x

y

Answer


{ 𝑥− 𝑦 ≤2𝑦<4 𝑥+1

-5 5

-5

5

x

y


{ 𝑥− 𝑦 ≤2𝑦<4 𝑥+1

Answer


{𝑦 ≥2|𝑥−3|−4

𝑦<− 23𝑥+1

-5 5

-5

5

x

y

-5 5

-5

5

x

y


{𝑦 ≥2|𝑥−3|−4

𝑦<− 23𝑥+1

-5 5

-5

5

x

y

Answer

Graph the feasible region and find the point that maximize the function:

{ 𝑦 ≥ 𝑥−2𝑥+2 𝑦 ≤8𝑦 ≥1𝑥≥0

-5 5

-5

5

x

y

-5 5

-5

5

x

y

Graph the feasible region and find the point that maximizes the function:

{ 𝑦 ≥ 𝑥−2𝑥+2 𝑦 ≤8𝑦 ≥1𝑥≥0

(0, 1)

(0, 5)

(4, 2)

(3, 1)

Answer


{−𝑥+2 𝑦 ≤4𝑥+𝑦 ≤8𝑦 ≥1𝑥≥2

-1 10-1

10

x

y

-1 10-1

10

x

y


{−𝑥+2 𝑦 ≤4𝑥+𝑦 ≤8𝑦 ≥1𝑥≥2

-1 10-1

10

x

y

(2, 1)

(2, 2)

(5, 4)

(7, 1)

Answer

The school that Danielle goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 7 senior citizen tickets and 3 child tickets for a total of $74. The school took in $135 on the second day by selling 14 senior citizen tickets and 5 child tickets. Write a system of equations to find the price of one senior citizen ticket and one child ticket?

The school that Danielle goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 7 senior citizen tickets and 3 child tickets for a total of $74. The school took in $135 on the second day by selling 14 senior citizen tickets and 5 child tickets. Write a system of equations to find the price of one senior citizen ticket and one child ticket?

Answer

Amanda and Eduardo each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Amanda spent $83 on 7 ft² of grass sod and 3 shrubs. Eduardo spent $118 on 8 ft² of grass sod and 6 shrubs. Find the cost of one ft² of grass sod and the cost of one shrub.

Write a system of equation to solve the problem.

Amanda and Eduardo each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Amanda spent $83 on 7 ft² of grass sod and 3 shrubs. Eduardo spent $118 on 8 ft² of grass sod and 6 shrubs. Find the cost of one ft² of grass sod and the cost of one shrub.

Write a system of equation to solve the problem.

Answer

Meg has three dogs – Skippy, Gizmo, and Chopper. The sum of the dogs’ weights is 148 pounds. If you add three times Skippy’s weight to Gizmo’s weight, the sum is 8 pounds less than Chopper’s weight. If you subtract one-third of Skippy’s weight from four times Gizmo’s weight, the result is equal to twice Chopper’s weight.Write a system of equations to find out how much each dog weighs? Then solve the system.

Meg has three dogs – Skippy, Gizmo, and Chopper. The sum of the dogs’ weights is 148 pounds. If you add three times Skippy’s weight to Gizmo’s weight, the sum is 8 pounds less than Chopper’s weight. If you subtract one-third of Skippy’s weight from four times Gizmo’s weight, the result is equal to twice Chopper’s weight.Write a system of equations to find out how much each dog weighs? Then solve the system.

Skippy: 12 poundsGizmo: 46 poundsChopper: 90 pounds

Answer

You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound and granola cost $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredient should you buy?

You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound and granola cost $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredient should you buy?

{2.5𝑝+2𝑟+4𝑔=80 𝑝+𝑟 +𝑔=30𝑝=2𝑟

Peanuts (p): 16 poundsRaisins (r): 8 poundsGranola (g): 6 pounds

Answer

You are making your summer movie plans and are working with following constraints:• It costs $8 to go to the movies at night.• It costs $5 to go to a matinee.• You want to go to at least as many night shows as matinees.• You want to spend at most $42What is the greatest number of movies you can see?

You are making your summer movie plans and are working with following constraints:• It costs $8 to go to the movies at night.• It costs $5 to go to a matinee.• You want to go to at least as many night shows as matinees.• You want to spend at most $42What is the greatest number of movies you can see?

{8𝑛+5𝑚≤ 42𝑛≥𝑚𝑛≥0𝑚≥0

1 2 3 4 5 6 7

1

2

3

4

5

6

7

Matinee

Night

6 Movies:3 night, 3 matinee4 night, 2 matinee

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Linear System of Equations Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices −213