Entry Task

Solve for y

1) 2x + -3y < 12

2) x > ½ y - 7

3.3 SYSTEMS OF INEQUALITIES

Learning Target:

I can solve Linear Systems of Inequalities by Graphing

Success Criteria: I will be able to graph 2 inequalities and find the “overlap”

Solving Systems of Linear Inequalities

1. We show the solution to a system of linear inequalities by graphing them.

a) This process is easier (but not required) if we put the inequalities into Slope-Intercept Form, y = mx + b.

b) Why?

c) If y < x then shade below the line

d) If y > x then shade above the line

Solving Systems of Linear Inequalities

2. Graph the line using the y-intercept & slope.

a) If the inequality is < or >, make the lines dotted.

b) If the inequality is < or >, make the lines solid.

Solving Systems of Linear Inequalities

3. The solution also includes points not on the line, so you need to shade the region of the graph:

Use a test point (0,0) if available.

What makes (0,0) unavailable?

Solving Systems of Linear Inequalities

Example: a: 3x + 4y > - 4

b: x + 2y < 2

Put in Slope-Intercept Form: ) 3 4 4

4 3 4

31

4

a x y

y x

y x

) 2 2

2 2

11

2

b x y

y x

y x

Solving Systems of Linear Inequalities

a:

dotted

shade above

b:

dotted

shade below

Graph each line, make dotted or solid and shade the correct area.

Example, continued:

3: 1

4 a y x 1

: 12

b y x

Solving Systems of Linear Inequalities

a: 3x + 4y > - 4

3: 1

4 a y x

Solving Systems of Linear Inequalities

a: 3x + 4y > - 4

b: x + 2y < 2

3: 1

4 a y x

1: 1

2 b y x

Solving Systems of Linear Inequalities

a: 3x + 4y > - 4

b: x + 2y < 2

The area between the green arrows is the region of overlap and thus the solution.

Things to remember…..There is one special case.

Sometimes you may have to reverse the direction of the inequality sign!!

That only happens when you

multiply or divide both sides of the inequality by a negative number.

Assignment #31 pg 153-154 (10pts)

Homework: P.153 #9,11,13,14,17,19,20,21,32, 37-45 odds, 46,47

Challenge: # 56