Graph Linear Inequalities in Two Variables


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1 Graph Linear Inequalities in Two Variables Name Goal Graph linear inequalities in two variables. VOCABLARY Linear inequality in two variables Graph of an inequality in two variables Example 1 Check solutions of a linear inequality Tell whether the ordered pair is a solution of 3x 4y > 9 a.(, 0) b. (, 1) a. Test (, 0): 3x 4y > 9 Write inequality. 3( ) 4( ) > 9 Substitute for x and for y. > 9 (, 0) a solution. b. Test (, 1): 3x 4y > 9 Simplify. Write inequality. 3( ) 4( ) > 9 Substitute for x and for y. > 9 Simplify. (, 1) a solution. GRAPHING A LINEAR INEQUALITY IN TWO VARIABLES Step 1 Graph the boundary line. Use a for < or >, and use a line for or. Step Test a point not on by checking whether the ordered pair is a solution of the inequality. Step 3 Shade the containing the point if the ordered pair a solution of the inequality. Shade the if he ordered pair solution.
2 Example Graph a linear inequality in two variables Graph the inequality y < 1 x Graph the equation y = 1 x + 4. The inequality is <, so use a line.. Test (0, 0) in y < 1 x + 4. < ( ) < 3. the halfplane that (0, 0) because (0, 0) a solution of the inequality. Graph a linear inequality in one variable Graph the inequality x Graph the equation x = 4. The inequality is, so use a line.. Test (0, 3) in x 4. You only substitute the because the inequality does not have the variable the halfplane that (0, 3), because (0, 3) a solution of the inequality.
3 YOUR TURN Graph the inequality. 1. y + 4x > 8. y < Solve Linear Systems of Linear Inequalities Goal Solve systems of linear inequalities in two variables. Your Notes VOCABULARY System of linear inequalities of a system of linear inequalities Graph of a system of linear inequalities
4 GRAPHING A SYSTEM OF LINEAR INEQUALITIES Step 1 each inequality. Step Find the of the graphs. The graph of the system is this intersection. Example 1 Graph a system of three linear inequalities Graph the system of inequalities. y > 1 Inequality 1 x 4 Inequality 3y < 6x 6 Inequality 3 Graph all three inequalities in the same coordinate plane. The graph of the system is the shown. The region is the line y = 1. The region is of the line x = 4. The region is the line 3y = 6x 6. YOUR TURN Graph the system of linear equations. 1. x + y 5. y > y < x + 3 y 4 3x + 4y 4
5 Example Write a system of linear inequalities Write a system of inequalities for the shaded region. Inequality 1 One boundary line for the shaded region is. Because the shaded region is the line, the inequality is. Inequality Another boundary line for the shaded region has a slope of and a yintercept of. So, its equation is. Because the shaded region is the line, the inequality is. The system of inequalities for the shaded region is: Inequality 1 Inequality YOUR TURN Write a system of inequalities that defines the shaded region. 1..
6 Example 3 You are planning a cookout. You figure that you will need at least 5 packages of hot dogs and hamburgers. A package of hot dogs costs $1.90 and a package of hamburgers costs $5.0. You can spend a maximum of $0 on the hot dogs and hamburgers. a. Let x represent the number of packages of hot dogs and let y represent the number of packages of hamburgers. Write a system of linear inequalities for the number of packages of each that can be bought. b. Graph the system of inequalities. c. Identify two possible combinations of packages of hot dogs and hamburgers you can buy.
7 PRACTICE Solving Systems of Linear Inequalities Name Date Period Tell whether the ordered pair is a solution of the system of inequalities. 1. (3, 0). (, ) 3. (, ) 1. (, ) Match the system of inequalities with its graph x+ y 3 x > y x 3 x < y x+ 3 x > 1 A. B. C. Graph the system of inequalities. 7. x y+ x+ y< 4 8. y x+ y 3 x y 9. x y< 4
8 Write a system of inequalities for the shaded region You need at least 4 hours to do your chores, which is cleaning out the garage and weeding the flower beds around your house. It is 1:30 p.m. on Sunday and your friend wants to go to the movies at 7:00 p.m. a. How much time do you have between now and 7:00 p.m. to do your chores? b. Let x represent the number of hours spent cleaning out the garage and let y represent the number of hours you can work on each chore if you go to the movies. c. Identify two possible combinations of time you can spend on each chore.
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