ALGEBRA TWO CHAPTER THREE SYSTEMS OF LINEAR EQUATIONS

ALGEBRA TWO CHAPTER THREE: SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES Section 3. 3 - Graphing and Solving Systems of Linear Inequalities

LEARNING GOALS Goal One - Graph a system of linear inequalities to find the solutions of the system. Goal Two - Use systems of linear inequalities to solve reallife problems.

Graphing a System of Linear Inequalities The following is a system of linear inequalities in two variables: x+y<6 Inequality 1 2 x - y > 4 Inequality 2 A solution of a system of linear inequalities is an ordered pair that is a solution of each inequality in the system. The graph of a system of linear inequalities is the graph of all solutions of the system.

Graphing a System of Linear Inequalities To graph a system of linear inequalities, do the following for each inequality in the system: STEP 1: Graph the line that corresponds to the inequality. Use a dashed line for and inequality with < or > and a solid line for an inequality with < or >. STEP 2: Lightly shade the half-plane that is the graph of the inequality. Colored pencils may help you distinguish the different half-planes. The graph of the system is the region common to all of the half-planes. If you used colored pencils, it is the region that has been shaded with every color.

Graphing a System of Linear Inequalities Graph the linear inequality system: Inequality 1 Inequality 2 y > -3 x - 1 y< x+2 The purple area represents all solutions for this linear inequality.

ASSIGNMENT READ & STUDY: pg. 156 -158. WRITE: pg. 159 -162. #13, #15, #17, #19, #27, #31, #37, #39, #41