Warm Up 1) Solve by graphing 2y = x + 3 2x + y = 4

2) Solve by substitution 2x + y = 5 4x + 2y = 5

3) Solve by elimination x – y = 7 3x – y = -19

Turn in stamp sheets today!

GRAPHING LINEAR

INEQUALITIES

Step 1) Put the inequalities into slope-intercept form.

y = mx + bslope

y-intercept

We show the solution to a linear inequality with a graph.

Step 2) Graph the line

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

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

Step 3) Shade the correct region of the graph:

a) Above the line b) Below the linefor y > or y . for y < or y ≤.

**This is because more then 1 ordered pair can be a solution!

Examples:

1) y > -5x + 4

Examples:

2) x < 4 3) y ≥ -3

Examples:4) 2x – 3y ≤ 6

**When you multiply or divide by a negative, flip the inequality sign.

Examples:

5) 3x + 2y < -2

SYSTEMS OF INEQUALITIES

We show the solution to a system of linear inequalities with a graph!

Steps to Graphing a System of Inequalities:1) Put the inequalities into slope-

intercept form.2) Decide if the lines should be dotted or

solid3) Shade above for y > or y , shade

below for y < or y ≤.4) Shade the overlapping section darker

to show where the solutions to both inequalities lie.

Example #1: a: 3x + 4y > - 4

b: x + 2y < 2

Put in Slope-Intercept Form:

3: 1

4 a y x

1: 1

2 b y x

#2 Graph the system of

linear inequalities.

x ³ –1

y > x – 2

#3x > -2y < 6-2x + y > -5

Let’s graph the next problem using the calculator

#4 y ≥ -x + 4y < 3x - 2

#5

x – y > 37x – y ≤ -3

#6

7x + 2y < -10-x + 2y ≤ 11

Classwork: Solving Systems of Inequalities Worksheet

Homework: 5.11