Chapter 4: Systems of Equations and Inequalities Section 4.7: Solving Linear Systems of Inequalities

Goal: To graph linear inequalities in two variables and to solve linear systems of inequalities in two variables

Section 4.7: Solving Linear Systems of Inequalities 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

Section 4.7: Solving Linear Systems of Inequalities Example 1 Solve each system of inequalities by graphing y ≥ 2x – 3 y < -x + 2

Section 4.7: Solving Linear Systems of Inequalities Example 2 Solve each system of inequalities by graphing y ≤ -x + 1 |x + 1| < 3

Section 4.7: Solving Linear Systems of Inequalities Example 3 Solve each system of inequalities by graphing y ≥ -3/4x + 1 y ≤ -3/4x – 2

Section 4.7: Solving Linear Systems of Inequalities 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

Section 4.7: Solving Linear Systems of Inequalities Example 5 Find the coordinates of the vertices of the figure formed by: 2x – y ≥ -1 x + y ≤ 4 x + 4y ≥ 4

Section 4.7: Solving Linear Systems of Inequalities HOMEWORK Page 180 Practice Exercises #10-30 (even)