Holt McDougal Algebra Solving Systems of Linear Inequalities Solve systems of linear inequalities. Objective

Holt McDougal Algebra Solving Systems of Linear Inequalities system of linear inequalities Vocabulary

Holt McDougal Algebra Solving Systems of Linear Inequalities When a problem uses phrases like “greater than” or “no more than,” you can model the situation using a system of linear inequalities. A system of linear inequalities is a set of two or more linear inequalities with the same variables. The solution to a system of inequalities is often an infinite set of points that can be represented graphically by shading. When you graph multiple inequalities on the same graph, the region where the shadings overlap is the solution region.

Holt McDougal Algebra Solving Systems of Linear Inequalities Graph the system of inequalities. Example 1A: Graphing Systems of Inequalities 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 McDougal Algebra Solving Systems of Linear Inequalities If you are unsure which direction to shade, use the origin as a test point. Helpful Hint

Holt McDougal 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 McDougal Algebra Solving Systems of Linear Inequalities Check It Out! Example 1a 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 McDougal Algebra Solving Systems of Linear Inequalities Graph each system of inequalities. y ≤ 4 2x + y < 1 For 2x + y < 1, graph the dashed boundary line y = –3x +2, and shade below it. For y ≤ 4, graph the solid boundary line y = 4, and shade below it. Check It Out! Example 1b The overlapping region is the solution region.

Holt McDougal Algebra Solving Systems of Linear Inequalities Systems of inequalities may contain more than two inequalities.

Holt McDougal 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 McDougal 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 McDougal Algebra Solving Systems of Linear Inequalities Graph the system of inequalities, and classify the figure created by the solution region. Check It Out! Example 3b y ≤ 4 y ≤ –x + 8 y ≥–1 y ≤ 2x + 2

Holt McDougal Algebra Solving Systems of Linear Inequalities Graph the solid boundary line y = 4 and shade to the below it. Graph the solid boundary line y = –1, and shade to the above it. Graph the solid boundary line y = –x + 8, and shade below it. Graph the solid boundary line y = 2x + 2, and shade below it. The overlapping region is the solution region. Check It Out! Example 3b Continued