Linear Inequalities in Two Variables PDF

e a r Lin a litie s q u Ine n Two i i a b l e s V a r Objectives  differentiates linear inequalities in two variables from linear equations in two variables. M8AL- IIa-2  Illustrates and graphs linear inequalities in two variables. M8AL-IIa-3 ...

e a r Lin a litie s q u Ine n Two i i a b l e s V a r Objectives  differentiates linear inequalities in two variables from linear equations in two variables. M8AL- IIa-2  Illustrates and graphs linear inequalities in two variables. M8AL-IIa-3  solves problems involving linear inequalities in two variables. M8AL-IIa-4  Expressions of the type x + 2y ≤ 8 and 3x – y > 6 are called linear inequalities in two variables. A solution of a linear inequality in two variables is an ordered pair (x, y) which makes the inequality true. Example: (1, 3) is a solution to x + 2y ≤ 8 since (1) + 2(3) = 7 ≤ 8. 3 Copyright © by Houghton Mifflin Company, Inc. All rights reserved.  NOTATION The symbol than”  is used to represent “less The symbol is used to represent “less than or equal to” The symbol  is used to represent “greater than” The symbol is used to represent “greater than or equal to”  PROPERTIES OF INEQUALITIES 1. If a, b, and c are real numbers, and if a and b, b  c thena  c 2. To solve inequalities, you can add or subtract the same number to both sides of the inequality: If a b ac , then bc. 3. To solve inequalities, you can multiply or divide by the same number on both sides. However, if you multiply or divide both sides by a negative number, you flip the inequality. Example: Multiply both sides of 26 by -1 and see what happens!  Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y or  then you shade above If it is < or  then you shade below the line EXAMPLE 1 Which ordered pair is a solution of 5x - 2y ≤ 6? A. (0, -3) B. (5, 5) C. (1, -2) D. (3, 3) EXAMPLE 2 Graph the inequality x ≤ 4 in a coordinate plane. HINT: Remember HOY VEX. Decide whether to 5 y use a solid or dashed line. Use (0, 0) as a test point. x Shade where the solutions will be. -5 -5 5 EXAMPLE 3 Graph 3x - 4y > 12 in a coordinate plane. Sketch the boundary line of the graph.  Find the x- and y y-intercepts and 5 plot them. Solid or dashed line? Use (0, 0) as a x test point. Shade where the solutions are. -5 -5 5 EXAMPLE 4: USING A NEW TEST POINT Graph y < 2/5x in a coordinate plane. Sketch the boundary line of the graph.  Find the x- and y-intercept and plot them. y  Both are the origin! 5 Use the line’s slope to graph another point. Solid or dashed line? x Use a test point OTHER than the origin. Shade where the solutions are. -5 -5 5 ACTIVITY ( BUDGET MATTERS) Directions: Use the situation below to answer the question below. Amelia was given by her mother Php320 to buy some food ingredients for “chicken adobo”. She made sure that it is good for 5 people. 1. SUPPOSE YOU WERE AMELIA. COMPLETE THE FOLLOWING TABLE WITH THE NEEDED DATA. INGREDIENTS QUANTITY COST PER UNIT ESTIMATED OR PIECE COST Chicken 1 kl ₱ 150 Soy sauce 1 pack ₱8 vinegar 1 pack ₱6 Garlic 1 cloves ₱5 Onion 2 pcs. ₱3 Black pepper 3 small packs ₱1 sugar ¼ kl ₱50 tomato 3 pcs ₱3 Green pepper 2 mini packs ₱1 potato ¼ kl ₱80 PROCESS QUESTIONS: 1. How do you feel while budgeting the amount of Php320 given by the mother of Amelia to buy ingredients for “Chicken Adobo”? 2. What is the total amount of the estimated cost for “chicken adobo”? 3. What can you say about Amelia? 4. Compare the amount of money given to Amelia and the estimated cost she used for ingredients for “chicken adobo”? Certain situations in real life can be modeled by linear inequalities.