13.7 – Graphing Linear Inequalities Are the ordered pairs a solution to the problem?

13.7 – Graphing Linear Inequalities

Are the ordered pairs a solution to the problem? 1

13

y x

3, 2

1,3

yes

no

2 2

43

3

11

32 3

3 11

13

Are the ordered pairs a solution to the problem? 1

13

y x

3,0

4, 3

yes

no

0 0

13

3

01

13

3

3 41

13

13.7 – Graphing Linear Inequalities

Are the ordered pairs a solution to the problem?

11

3y x

3, 2

1,3

3,0

yes

yes

4, 3

2 2 4

33

0 01

33

no

no

no

no yes

13.7 – Graphing Linear Inequalities

Graph the solution.

11

3y x

3, 2

1,3

3,0

4, 3

2 2 4

33

0 01

33

yes

yes no

no

no

no yes

13.7 – Graphing Linear Inequalities

Graph the solution.

11

4y x

1, 4

2,2

34

4

12

2

no

yes

13.7 – Graphing Linear Inequalities

Graph the solution.

3 2 10x y

4,3

0,0

3 1

0 5

no

yes

35

2y x

13.7 – Graphing Linear Inequalities

Graph the solution.

3y x

2,2

3,3

2 6

3 9

no

yes

13.7 – Graphing Linear Inequalities

Graph the solution.

3 5 10 0x y

0,0

2, 3

0 2

43

5

yes

no

32

5y x

13.7 – Graphing Linear Inequalities

14.1 – Solving Systems of Linear Equations by Graphing

3 3 0

2

x y

x y

A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed.

0

2 10

x y

x y

7 1

4

y x

y

72

92

432

y x

y x

y x

Determine whether (3, 9) is a solution of the following system.

5 2 3

3

x y

y x

5 3 2 39

15 18 3 3 3

9 33

9 9

Both statements are true, therefore (3, 9) is a solution to the given system of linear equations.

14.1 – Solving Systems of Linear Equations by Graphing

Determine whether (3, -2) is a solution of the following system.

2 8

3 4

x y

x y

2 3 2 8

6 2 8 8 8

3 23 4

3 6 4

Both statements are not true, therefore (3, -2) is not a solution to the given system of linear equations.

3 4

14.1 – Solving Systems of Linear Equations by Graphing

Solve the system of equations by graphing

13

3

2 4

y x

y x

: 3, 2Solution

2 2 3 4

2 2

12 3 3

3

2 2

14.1 – Solving Systems of Linear Equations by Graphing

Solve the system of equations by graphing

4 1

3

y x

y

: 1,3Solution

3 3 3 4 1 1

3 3

14.1 – Solving Systems of Linear Equations by Graphing

Solve the system of equations by graphing

2 0

3x y

x y

: 1, 2Solution

3 3

2 1 2 0

0 0

3y x

1 2 3

2y x

14.1 – Solving Systems of Linear Equations by Graphing

Special Systems of Linear EquationsConsistent system has at least one solution.

Inconsistent system has no solution.

Independent equations have different graphs.

Dependent equations have identical graphs.

Consistent system

Independent equations

14.1 – Solving Systems of Linear Equations by Graphing

Special Systems of Linear EquationsConsistent system has at least one solution.

Inconsistent system has no solution.

Independent equations have different graphs.

Dependent equations have identical graphs.

Inconsistent system

Independent equations

14.1 – Solving Systems of Linear Equations by Graphing

Special Systems of Linear EquationsConsistent system has at least one solution.

Inconsistent system has no solution.

Independent equations have different graphs.

Dependent equations have identical graphs.

Consistent system

Dependent equations

14.1 – Solving Systems of Linear Equations by Graphing