Solving Linear Inequalities Objectives To graph and solve
Solving Linear Inequalities Objectives: • To graph and solve linear inequalities with 2 variables • To graph and solve systems of linear inequalities with 2 variables
Key Terms • Linear Inequality – Similar to a linear equation, but the equal sign is replaced with an inequality symbol • <, <, >, > • Solution of Linear Inequality – Is any ordered pair that makes the inequality true
EX. 1 )Identifying Solutions • Tell whether the ordered pair is a solution A. (7, 3); y < x – 1 B. (4, 5) ; y > 3 x + 2
Ex. 2 a) Graphing Linear Inequalities • y < 3 x + 4 Steps: 1. Isolate y 2. Think of slope intercept form to graph a) < or > are dashed b) < or > are solid 3. Shade and check
Ex. 2 b) Graphing Linear Inequalities • 3 x +2 y > 6 Steps: 1. Isolate y 2. Think of slope intercept form to graph a) < or > are dashed b) < or > are solid 3. Shade and check
Writing and Inequality
Homework • Practice 5 -5 (page 364) – Day 1 • #’s 1 -11 skip 9 – Day 2 • #’s 12 -21 skip 19
Solving Systems of Linear Inequalities Key Terms • System of linear inequalities – Set of 2 or more linear inequalities containing 2 or more variables • Solutions of systems of linear inequalities – All of the ordered pairs that satisfy all the linear inequalities in the system
Ex 1) Identify Solutions of the Systems • (2, 1) y < -x + 4 y < x +1 • (2, 0) y > 2 x y < x +1
Ex 2) Solving a System of Inequalities Graph and list a solution y < -2 x + 3 y > ½ x -2
Ex 3 a) Solving a System of Inequalities Graph and list a solution y < 2 x - 3 y > 2 x + 2
Ex 3 b) Solving a System of Inequalities Graph and list a solution y>x-3 y<x+1
Ex 3 c) Solving a System of Inequalities Graph and list a solution y < -3 x - 2 y < -3 x + 4
Practice Solving a System of Inequalities Graph and list a solution 1. y < x + 1 y>2 2. y > 2 x + 3 y > 2 x
Homework • Practice 5 -6 (page 370) – Day 1 • #’s 1 -14 – Day 2 • #’s 16 -28
- Slides: 15