College Prep Unit 4: Systems of Equations and Inequalities ...

College Prep Unit 4: Systems of Equations and Inequalities

Ms. Talhami 1

College Prep Unit 4: Systems of Equations

and Inequalities

Name_________________


Ms. Talhami 2

Helpful Vocabulary Word Definition/Explanation Examples/Helpful Tips


Ms. Talhami 3

Proportions Vocabulary Definition/Explanation Examples

Proportion


Ms. Talhami 4


Ms. Talhami 5

Direct Variation Vocabulary Definition/Explanation

Direct Variation

“varies directly”

Direct Variation Equation _________________________ Constant of Variation _________________________ Graphs of Direct Variations Tables of Direct Variations a) b) a) b)

Examples: 1) The cost of a taxi fare varies directly as the distance travelled. When the distance is 60 km, the cost is $35. Find the cost when the distance is 95 km. 2) The total cost of filling up your car with gas varies directly with the number of gallons of gasoline that you are purchasing. If a gallon of gas costs $2.25, how many gallons could you purchase for $18?


Ms. Talhami 6

Practice


Ms. Talhami 7


Ms. Talhami 8

Systems of Equations Vocabulary Definition/Explanation

System of Equations

Methods to Solving Linear Systems

Graphing Elimination Substitution

Solve Linear Systems by Graphing


Ms. Talhami 9

9) ! = − $

% & + 1

! = − )$ & + 1


Ms. Talhami 10

Extra Practice

Methods to Solving Linear Systems

Graphing Elimination Substitution

Solve Linear Systems by Elimination Examples: 1) 2& + 3! = 20 2) & + 2! = 11 −2& + ! = 4 −3& + ! = −5

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Equations in Standard FormID: 1

Name___________________________________

Period____Date________________©E F2B00143w oKMuItaaj 8SWoQfFtFwNa6rYeF 6LGLUCB.L i sAylCl8 srIi8gphBtwsR NrJeLsfepryvUegdF.m

Solving Systems by Graphing

Solve each system by graphing.

1)

2

x +

y = 1

x − 2

y = 8

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

2)

3

x + 2

y = 4

x + 2

y = −4

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

3)

4

x +

y = 1

x +

y = −2

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

4)

x + 3

y = −9

5

x + 3

y = 3

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-1-

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Equations in Standard FormID: 1

Name___________________________________

Period____Date________________©E F2B00143w oKMuItaaj 8SWoQfFtFwNa6rYeF 6LGLUCB.L i sAylCl8 srIi8gphBtwsR NrJeLsfepryvUegdF.m

Solving Systems by Graphing

Solve each system by graphing.

1)

2

x +

y = 1

x − 2

y = 8

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

2)

3

x + 2

y = 4

x + 2

y = −4

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

3)

4

x +

y = 1

x +

y = −2

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

4)

x + 3

y = −9

5

x + 3

y = 3

x

y

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-1-


Ms. Talhami 11

Practice

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Kuta Software - Infinite Algebra 1 Name___________________________________

Period____Date________________Solving Systems of Equations by Elimination

Solve each system by elimination.

1)

−4

x − 2

y = −12

4

x + 8

y = −24

2)

4

x + 8

y = 20

−4

x + 2

y = −30

3)

x −

y = 11

2

x +

y = 19

4)

−6

x + 5

y = 1

6

x + 4

y = −10

5)

−2

x − 9

y = −25

−4

x − 9

y = −23

6)

8

x +

y = −16

−3

x +

y = −5

7)

−6

x + 6

y = 6

−6

x + 3

y = −12

8)

7

x + 2

y = 24

8

x + 2

y = 30

9)

5

x +

y = 9

10

x − 7

y = −18

10)

−4

x + 9

y = 9

x − 3

y = −6

11)

−3

x + 7

y = −16

−9

x + 5

y = 16

12)

−7

x +

y = −19

−2

x + 3

y = −19

-1-


Ms. Talhami 12


Ms. Talhami 14

How to Graph Inequalities

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Period____Date________________Graphing Linear InequalitiesSketch the graph of each linear inequality.

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Ms. Talhami 15


Ms. Talhami 16

Solve Inequality Systems by Graphing

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Period____Date________________Systems of Inequalities

Sketch the solution to each system of inequalities.

1)

y

>

4

x

− 3

y

≥

−2

x

+ 3

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

2)

y

≥

−5

x

+ 3

y

> −2

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

3)

y

< 3

y

≤

−

x

+ 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

4)

y

≥

x

− 3

y

≥

−

x

− 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-1-


Ms. Talhami 17


Ms. Talhami 18

More Practice

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Period____Date________________Solving Systems of InequalitiesSketch the solution to each system of inequalities.

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-1-


Ms. Talhami 19


Ms. Talhami 20

Extra Graph Paper


Ms. Talhami 21

Extra Graph Paper

College Prep Unit 4: Systems of Equations and Inequalities ...

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