6.6 Systems of Linear Inequalities

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# 6.6 Systems of Linear Inequalities - PowerPoint PPT Presentation

6.6 Systems of Linear Inequalities. Standard: SWBAT solve a system of two linear inequalities in two variables and to sketch the solution sets. Mini Quiz 54. 1. Determine whether the point P is a solution of the linear inequality 2. Solve the linear system (use any method).

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### 6.6 Systems of Linear Inequalities

Standard: SWBAT solve a

system of two linear inequalities in two variables and to sketch the solution sets.

Mini Quiz 54

1. Determine whether the point P is a solution of the linear inequality

2. Solve the linear system (use any method).

3x + 4y = 5

-2x + y = 4

Quick Review

=

• What is the difference between an equation and an inequality? Which one is shaded?
• When is the line solid?
• When is the line dashed (dotted)?
• How do you figure out where to shade?

Graph this inequality:

y > x – 2

m = 1

b = -2

<,>

Inequality

≤, ≥

<, >

Pick a point to plug in.

Check if it’s a solution

1. (4, 10)

9x – y ≥ 23

5x + 0.2y ≥ 20

2. (2, -1)

y ≤ 4x + 1

y > -x + 2

5(4) + 0.2(10) ≥ 20

20 + 2 ≥ 20

22 ≥ 20 

9(4) – 10 ≥ 23

36 – 10 ≥ 23

26 ≥ 23 

YES

-1 ≤ 4(2) + 1

-1 ≤ 8 + 1

-1 ≤ 9 

-1 > -(2) + 2

-1 > 0 

NO

Graphing Systems of Linear Inequalities

Graph each system

3. y < 2 4. y > x – 2

x ≥ -1y ≤ - ½ x + 3

Graphing Systems of Linear Inequalities

Graph each system

5. y > 2x – 5 6. y ≥ -x + 2

3x + 4y < 122x + 4y < 4

Writing Systems of Linear Inequalities Equation

Write the inequalities for each system

7. 8.

Wrap Up

Checking solutions – have to work for both equations

Graphing Inequalities

dashed (dotted) - < or >

solid - ≤ or ≥