Chapter 4: Systems of Equations

and Inequalities

Section 4.7: Solving Linear Systems of 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

InequalitiesHOMEWORK

Page 180Practice Exercises

#10-30 (even)