Review Lesson Vocabulary TwoVariable Inequality An inequality using

Review Lesson

Vocabulary • Two-Variable Inequality: An inequality using two different variables Example: 2 x + 4 y ≤ 10 • Strict Inequality: Inequalities using the following signs > or < Example: 2 x > 4 y -5 • Half-Plane: The coordinate plane divided into two halves by a boundary line where one half represents the solutions of the inequality. Example:

Solve Two-Variable Equations 1) Solve 10 x+2 y=6 for y. 10 x + 2 y = 6 -10 x 2 y = -10 x + 6 2 2 y = -5 x + 3 Subtract 10 x from both sides Divide by 2 on both sides Simply both sides

Solve Two-Variable Equations 1. Solve 25 x + 5 y = 100 for y. 2. Solve 3 x + 24 y = 9 for x. 3. Solve 30 y + 60 x = 2400 for y. 4. Solve x + y = 4 for x. 5. Solve 2 y – 6 y = 33 for y.

Solve Two-Variable inequalities for x or y 1) Solve 10 x+2 y > 6 for y. 10 x + 2 y > 6 -10 x 2 y > -10 x + 6 2 2 y > -5 x + 3 Subtract 10 x from both sides Divide by 2 on both sides Simply both sides

Solve Two-Variable inequalities for x or y 1) Solve 10 x - 2 y ≤ 6 for y. 10 x - 2 y ≤ 6 -10 x Subtract 10 x from both sides -2 y ≤ -10 x + 6 Divide by 2 on both sides -2 -2 **Notice the sign flipped. When you divide by a negative # or multiply by a negative # you have to flip the sign!!! y ≥ 5 x - 3 Simply both sides

Solve Two-Variable inequalities for x or y 1) Solve 25 x + 5 y > 100 for y. 1) Solve 3 x + 24 y < 9 for x. 1) Solve -30 y + 60 x ≤ 2400 for y. 4. Solve x + y ≥ 4 for x. 5. Solve 2 y – 6 y < 33 for y.

Graph y = mx+b y = -5 x + 3 Solve 10 x+2 y=6 for y. 10 x + 2 y = 6 -10 x 2 y = -10 x + 6 2 2 y = -5 x + 3 Y-intercept = b b = +3 Slope = m m = -5 m = - 3 = -5 0. 6 -3 0. 6

Graph y = mx + b 1) 4 x + 3 y = 36 2) 10 y – 50 x = 200 3) 98 x – 2 y = 10 4) 5 y = 10 x – 50 5) 6= 3 x + 20 y

Solving Systems of Linear Inequalities

International Travel and Cell Phone Bills • You and your friend are traveling to another country, SPAIN! • You have a cell phone plan with Verizon and your friend with Sprint • Using a system of inequalities we can determine who gets the better pricing and what solutions work for both you and your friend

To solve systems of inequalities do the following: A) Create inequalities if not provided with one. B) Solve each inequality for the variable y. C) Graph each inequality & shade in the solution set for each inequality. D) Overlap the two graph inequalities. E) Determine the solutions of the system.

Plans Verizon Sprint • https: //www. verizonwireless. co m/solutions-andservices/international-travel/ • https: //support. sprint. com/supp ort/international/roaming/Barce lona%2 C%20 Spain/dvc 10400001 prd • Going to focus on Data and Talk • 100 MB of data • Going to focus on Data and Talk • 100 MB of Data

Create our System of Inequalities x = talk y = data Verizon Sprint 1. 79 x +. 10 y ≤ 100 . 2 x +. 15 y ≤ 100 System of Inequalities 1. 79 x +. 10 y ≤ 100. 2 x +. 15 y ≤ 100

Solve each inequality for y. Verizon 1. 79 x +. 10 y ≤ 100 -1. 79 x. 10 y ≤ -1. 79 x +100. 10 y ≤ -17. 9 x + 1000 Sprint . 2 x +. 15 y ≤ 100 -. 2 x. 15 y ≤ -. 2 x +100. 15 y ≤ 1. 3 x +667

Graph each inequality Verizon Sprint

Overlap the two graphed inequalities

Determine the solutions of the system. Red shaded area represents all the solutions for the Verizon Inequality. No solution in the unshaded area Overlapped shaded area represents Solutions for both inequalities Blue shaded area represents all the solutions for the Sprint Inequality.

Essential Questions 1. Pick one problem from your practice worksheet. • Why does the solution set you found make sense? • Describe a scenario that could apply to the problem you chose. 2. Why do you think we exclude strict inequalities?

The End You all are awesome!!! Have a great rest of your day!!