+ Unit 1 – First-Degree Equations and Inequalities Chapter 3 – Systems of Equations and Inequalities 3.3 – Solving Systems of Inequalities by Graphing.

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Presentation transcript:

+ Unit 1 – First-Degree Equations and Inequalities Chapter 3 – Systems of Equations and Inequalities 3.3 – Solving Systems of Inequalities by Graphing

+ In this section we will review how to: Solve systems of inequalities by graphing Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities

+ 3.3 – Solving Systems of Inequalities by Graphing System of Inequalities – Two or more inequalities with the same variables Solving a system of inequalities – Finding all of the ordered pairs that satisfy all of the inequalities in the system. Represented by the intersection of the graphs of the inequalities

+ 3.3 – Solving Systems of Inequalities by Graphing Example 1 Solve each system of inequalities by graphing y ≥ 2x – 3 y < -x + 2

+ 3.3 – Solving Systems of Inequalities by Graphing Example 2 Solve each system of inequalities by graphing y ≤ -x + 1 |x + 1| < 3

+ 3.3 – Solving Systems of Inequalities by Graphing Example 3 Solve each system of inequalities by graphing y ≥ -3/4x + 1 y ≤ -3/4x – 2

+ 3.3 – Solving Systems of Inequalities by Graphing Example 4 Medical professionals recommend that patients have a cholesterol level below 200 milligrams per deciliter (mg/dL) of blood and a triglyceride level below 150 mg/dL. Write and graph a system of inequalities that represents the range of cholesterol levels and triglyceride levels for patients. Let c represent the cholesterol levels and t represent the triglyceride levels.

+ 3.3 – Solving Systems of Inequalities by Graphing Sometimes the graph of a system of inequalities forms a polygonal region. To find the vertices of the region, determine the coordinates of the points at which the boundaries intersect

+ 3.3 – Solving Systems of Inequalities by Graphing Example 5 Find the coordinates of the vertices of the figure formed by: 2x – y ≥ -1 x + y ≤ 4 x + 4y ≥ 4

+ 3.3 – Solving Systems of Inequalities by Graphing HOMEWORK Page 133 #10-22 (even), #32-36 (even)