Systems Of Linear Inequalities

Solid because the inequality includes "equal to"

Solid because it is "greater than"

Dashed because the slope is negative

Dashed because y-intercept is negative

Below the line because the inequality includes "less than"

Below because it is a negative slope

Above because the y-intercept is positive

Above because the inequality does not include "equal to"

$$y>2x+1$$  

$$y>\frac{1}{2}x+1$$  

$$y<2x+1$$  

$$y<\frac{1}{2}x+1$$  

$$y<2x-4$$  

$$y<\frac{1}{2}x-4$$  

$$y>2x-4$$  

$$y>\frac{1}{2}x-4$$  

$$y<x-2$$  

$$y\ge-3x+2$$  

$$y\ge-1x-2$$  

$$y\ge-\frac{1}{3}x+2$$  

$$y<-\frac{1}{2}x+3$$  

$$y<3x-4$$  

$$y<-2x+3$$  

$$y<\frac{1}{3}x-4$$  

satisfy both inequalities

satisfy at least one inequality

not satisfy either inequality.

Satisfy means make it a true statement.

4>3 is a true statement.

yes

no

no solution

yes

no

no solution

Dashed line, shade above

Dashed line, shade below

Solid line, shade above

Solid line, shade below

Dashed line, shade above

Dashed line, shade below

Solid line, shade above

Solid line, shade below

y < 2x - 5

y > 2x - 5

y ≤ 2x - 5

y ≥ 2x - 5

y < -4 

y > -4

y ≤ -4 

y ≥ -4 

y < 3/5x - 5

y > 3/5x - 5

y ≤ 3/5x - 5

y ≥ 3/5x - 5

$$y<\frac{2}{3}x+1$$
$$y\ge-5x+10$$

$$y<\frac{2}{3}x+1$$
$$y\le-5x+10$$

$$y>\frac{2}{3}x+1$$
$$y\ge-5x+10$$

(-10,-5)

(-20,25)

(40,30)

(40,-10)

(-5,4)

(-5,-2)

(0,10)

(5,10)

(0,-5)