We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byJacob Baldwin
Modified over 3 years ago
© Boardworks 2012 1 of 13 Graphing inequalities in two variables
© Boardworks 2012 2 of 13 Inequalities in two variables Linear inequalities can be given in two variables x and y. x + y > 3 Can you name a pair of values that satisfy the inequality? x = 1and y = 4 x = 4and y = 5 x = –1and y = 5 These solutions are usually written as coordinate pairs as (1, 4), (–1, 5), (4, 5), (12, –6). The whole solution set can be represented using a graph. For example, Some example solution pairs are: x = 12and y = –6
© Boardworks 2012 3 of 13 Graphing the inequality We can represent all the points where the x -coordinate and the y -coordinate add up to 3 with the line x + y = 3. 012345 6 –1–2–3–4–5–6 1 2 3 4 5 –2 –4 –3 –5 –1 y x The region where x + y > 3 does not include points where x + y = 3 and so we draw this as a dotted line. We need to decide which part of the graph is the solution set. How can we check?
© Boardworks 2012 4 of 13 Checking the origin Is the origin in the region x + y > 3? Substitute x = 0 and y = 0 into the inequality x + y > 3: 0 + 0 > 3 0 > 2 0 is not greater than 2, so the origin is not in the solution region. The region representing x + y > 3 is therefore the region above the line. Choose a point off the line and see if it satisfies the inequality. It is often easiest to check the origin, (0, 0). 012345 6 –1–2–3–4–5–6 1 2 3 4 5 –2 –4 –3 –5 –1 y x x + y > 3 x + y < 3
© Boardworks 2012 5 of 13 Inequalities in two variables 012345 6 –1–2–3–4–5–6 1 2 3 4 5 –2 –4 –3 –5 –1 y x Draw the line 2 y – x = 4. 2(0) – 0 = 0 < 4 This is true, so we know that (0, 0) is in the solution set. The solution set is therefore the region below the line. Represent the solutions to the inequality 2 y – x < 4 on a graph. Check if the origin is in the region by substituting x = 0 and y = 0 into the inequality 2 y – x < 4: 2 y – x < 4
© Boardworks 2012 6 of 13 If 20 cars were already on board, how many more trucks could the ferry carry? A ferry cannot hold more than 30 tons. If it holds x cars weighing 1 ton each and y trucks weighing 3 tons each, write down an inequality in x and y. Cars and trucks x + 3 y 30 Substitute into x + 3 y 30 and solve for y, 20 + 3 y 30 subtract 20 from both sides: 3 y 10 divide both sides by 3: y 3.3 (to nearest tenth) The ferry can hold 3 more trucks.
© Boardworks 2012 7 of 13 Cars and trucks Show the possible numbers of cars and trucks that the ferry can carry on a graph. Start by drawing the x -axis between 0 and 30 and y -axis between 0 and 10. Next, draw the line x + 3 y = 30. x y 0 10 30 x + 3 y = 30 10 20 This point represents 20 cars and 3 trucks. The points on the graph represent the solution set.
© Boardworks 2012 8 of 13 Uncles and aunts I have more uncles than aunts. Two of my aunts live together. Even if all my uncles and aunts brought a friend each, they still wouldnt have enough people for a soccer team. How many uncles and aunts does the girl have? Use the inequality graphing tool on the next slide to confirm your answer.
© Boardworks Ltd of 50 A4 Inequalities KS4 Mathematics.
8/8/ Inequalities. 8/8/ Bumper Cars You must be at least 130cm tall to ride the bumper cars. This can be represented by the inequality.
9.3 Linear Inequalities in Two Variables. Objective 1 Graph linear inequalities in two variables. Slide
Pre-Algebra 10-6 Systems of Equations Learn to solve systems of equations.
Chapter 3 Section 5. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graphing Linear Inequalities in Two Variables Graph linear inequalities.
Section 4Chapter 3. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 3 Linear Inequalities in Two Variables Graph linear inequalities.
1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 3 Linear Inequalities in Two Variables Graph linear inequalities in two variables.
EXAMPLE 1 Use the substitution method Solve the linear system: y = 3x + 2 Equation 2 Equation 1 x + 2y = 11 Solve for y. Equation 1 is already solved for.
CHAPTER TWO: LINEAR EQUATIONS AND FUNCTIONS ALGEBRA TWO Section Linear Inequalities in Two Variables.
Graphing Linear Inequalities in Two Variables Section 6.5 Algebra I.
Chapter 3 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
6-6 Solving Linear Inequalities A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution.
4.1 Solving Linear Inequalities Objective: Solve and graph simple and compound inequalities in one variable.
8.8 Linear Inequalities, Systems, and Linear Programming.
Solve Linear Systems by Substitution January 28, 2014 Pages
4.4 Solving Multi-step Inequalities. 4.4 – Solving Multi-step Inequal. Goals / “I can…” Solve multi-step inequalities with variables on one side Solve.
Notes Over 2.6 Checking Solutions of Inequalities Check whether the given ordered pairs are solutions of the inequality.
Solve a two-step inequality EXAMPLE 1 3x – 7 < 8 Write original inequality. 3x < 15 Add 7 to each side. x < 5 Divide each side by 3. ANSWER The solutions.
© Boardworks Ltd of 56 © Boardworks Ltd of 56 AS-Level Maths: Core 1 for Edexcel C1.3 Algebra and functions 3 This icon indicates the slide.
Holt McDougal Algebra Solving Linear Inequalities 5-5 Solving Linear Inequalities Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation.
GOAL Graphing linear inequalities in two variables.
Solving Systems of Linear Equations Addition (Elimination) Method Tutorial 14c.
Chapter 3 Section 4 Copyright © 2011 Pearson Education, Inc.
Solve an inequality using multiplication EXAMPLE 2 < 7< 7 x –6 Write original inequality. Multiply each side by –6. Reverse inequality symbol. x > –42.
Systems of Equations 7-4 Learn to solve systems of equations.
Math Pacing Graphing Inequalities in Two Variables.
EXAMPLE 2 Solve an absolute value inequality Solve x – 5 7. Graph your solution. Write original inequality. | x – 5 | 7 x – 5 7 or x – 5 7 Rewrite.
§ 4.4 Linear Inequalities in Two Variables. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 4.4 Linear Inequalities in Two Variables Let’s consider.
Use graphing to solve this system. 1. y = 2x y = -x + 3 Use substitution to solve this system. 2. y = x-2 -2x -4y = 4 Use elimination to solve this system.
© Boardworks of 19 Solving linear inequalities.
Warm-Up Solve the following Inequalities:
EXAMPLE 1 Solve an equation with variables on both sides 7 – 8x = 4x – 17 7 – 8x + 8x = 4x – x 7 = 12x – = 12x Write original equation. Add.
Graphing Linear Inequalities in 2 Variables By Tristen Billerbeck.
One Step Equations and Inequalities Review. Review Remember: Addition and subtraction are inverse operations and multiplication and division are inverse.
Use addition to eliminate a variable EXAMPLE 1 Solve the linear system: 2x + 3y = 11 –2x + 5y = 13 Equation 1 Equation 2 SOLUTION Add the equations to.
4.5 Systems of Linear Inequalities 1 Linear Inequalities in Two Variables The graph of the solutions of a linear inequality in two variables is a half-plane.
Systems of Linear Inequalities. Two or more linear inequalities together form a system of linear inequalities.
Graphing Linear Inequalities in Two Variables A linear inequality in two variables takes one of the following forms: The solution of a linear inequality.
Graphical Solutions of a “Less Than” Linear Inequality in One Variable To determine the solutions of the inequality, graph the functions and. Sketch the.
1 Math Pacing Graphing Linear Equations. Equations as Relations A linear equation can be written in the standard form of a linear equation: Ax + By =
Graphing Linear Inequations y > y is greater than all points above the line are a solution y < y is less than all points below the line are a solution.
Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =
Solving Systems with 2 Variables U3.1. Vocabulary A system of linear equations in two variables x and y, also called a linear system, consists of two.
6.5 Graphing Linear Inequalities in Two Variables 7.6 Graphing Linear Inequalities System Objectives 1. Graph linear inequalities. 2. Graph systems of.
4.2 Solving Inequalities using ADD or SUB. 4.2 – Solving Inequalities Goals / “I can…” Use addition to solve inequalities Use subtraction to solve.
Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.
Chapter 6 – Solving and Graphing Linear inequalities 6.5 – Graphing Linear Inequalities in Two Variables.
Do Now Draw the graph of: 2x – 4y > 12. Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y <
Graphing Inequalities EXAMPLE 1 InequalityGraphVerbal Phrase a. y < 7 b. q 3 c. x > –5 d. h All numbers less than 7 All numbers less than or.
Use graphing to solve. 1. x + y = 6 3x – 4y = 4 Use substitution to solve. 2. y= 2x – 4 x – 5y = 14 Use elimination to solve. 3. 2x – 5y = 1 3x – 4y =
© 2017 SlidePlayer.com Inc. All rights reserved.