Holt Algebra Solving Systems of Linear Inequalities Solve systems of linear inequalities by graphing and shading Objective

Holt Algebra Solving Systems of Linear Inequalities Example 1A: Graphing Systems of Inequalities Graph the system of inequalities. 2x + y > 1.5 x – 3y < 6 For x – 3y < 6, graph the dashed boundary line y = – 2, and shade above it. For 2x + y > 1.5, graph the dashed boundary line y = –2x + 1.5, and shade above it. The overlapping region is the solution region.

Holt Algebra Solving Systems of Linear Inequalities Graph each system of inequalities. Example 1B: Graphing Systems of Inequalities y ≥ –1 y < –3x + 2 For y < –3x + 2, graph the dashed boundary line y = –3x + 2, and shade below it. For y ≥ –1, graph the solid boundary line y = –1, and shade above it.

Holt Algebra Solving Systems of Linear Inequalities Graph the system of inequalities, and classify the figure created by the solution region. Example 3: Geometry Application x ≥ –2 y ≥ –x + 1 x ≤ 3 y ≤ 4

Holt Algebra Solving Systems of Linear Inequalities Graph the solid boundary line x = –2 and shade to the right of it. Graph the solid boundary line x = 3, and shade to the left of it. Graph the solid boundary line y = –x + 1, and shade above it. Graph the solid boundary line y = 4, and shade below it. The overlapping region is the solution region. Example 3 Continued

Holt Algebra Solving Systems of Linear Inequalities 1. Graph the system of inequalities. Notes #1 y ≥ –x + 2 y < – 3 For y < – 3, graph the dashed boundary line y = – 3, and shade below it. For y ≥ –x + 2, graph the solid boundary line y = –x + 2, and shade above it. The overlapping region is the solution region.

Holt Algebra Solving Systems of Linear Inequalities Notes #2 2. Graph the system of inequalities and classify the figure created by the solution region. y ≤ x – 2 x ≤ 4 y ≥ –2x – 2 x ≥ 1 trapezoid

Holt Algebra Solving Systems of Linear Inequalities Notes #3 3. The cross-country team is selling water bottles to raise money for the team. The price of the water bottle is $3 for students and $5 for everyone else. The team needs to raise at least $400 and has 100 water bottles. Write and graph a system of inequalities that can be used to determine when the team will meet its goal.

Holt Algebra Solving Systems of Linear Inequalities Notes #3 x + y ≤ 100 3x + 5y ≥ 400