Systems of Linear Inequalities Coordinate algebra

Standard and Learning Targets A.REI.12 Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. SWBAT graph a linear inequality on a coordinate plane SWBAT graph a systems of linear inequalities and find a solution

Graphing Linear Inequalities Step 1: Graph the BOUNDARY, which is the equation of the line. Step 2: By looking at our INEQUALITY SIGN, determine how to draw the line. > or < will give us a DOTTED LINE line. or will give us a SOLID LINE line. Step 3: Determine which side of the boundary to SHADE in order to represent our RANGE OF SOLUTIONS

How do we know which side of the boundary to shade? Step 1: We must pick an ordered pair to TEST. Step 2: We must SUBSTITUTE the ordered pair into our inequality to determine if it makes a TRUE statement or a FALSE statement. Step 3: If our statement is true we will shade TOWARDS the point. If our statement is false we will shade AWAY the point.

Example 1: Graph the Inequality y > -3x + 2.

Guided Practice

Solving SYSTEMS of Inequalities We have learned that the solution of a linear system of equations occurs where the two lines INTERSECT. Likewise, the solution of system of linear inequalities occurs where the two regions OVERLAP. Any ordered pair that lies in the REGION OF OVERLAP is a solution.

Solving Systems of Inequalities Step 1: Put all inequalities in y = mx +b form. Step 2: Graph the LINES. Step 3: Shade the REGION OF SOLUTION for each inequality. (Use different colors for each. Darken the region where color overlaps.) The overlap of the two regions is your SOLUTION!

Example 1: Solve the system of inequalities

Example 2: Solve the system of inequalities

Guided Practice

Independent Practice Work in groups of 3 (practice problems in your notes)

Exit Ticket 1. Solve the system of inequalities by graphing. Then, identify two solutions! y > 4x − 3 y ≥ −2x + 3