2.7 Two-variable inequalities (linear) 3.3 Systems of Inequalities Algebra 2 2.7 Two-variable inequalities (linear) 3.3 Systems of Inequalities

Objectives By the end of class, I should be able to: Graph two variable inequalities Solve systems of inequalities Graph systems of inequalities by hand and using technology to represent the solutions

Check your Skills Choose any method to solve

Graph the line y = 2x + 3 on graph paper. a. Plot each point listed below. (-2,-3) (-2,-1) (-1,-1) (-1,5), (0,4) (0,5) (1,6) (2,3) (2,7) b. Classify each point as on the line, above the line, or below the line.

Are all the points that satisfy y > 2x + 3 above, below or on the line?

Graphing Linear Inequalities Step 1: Graph the boundary line Step 2: Solid or dotted line? Less than /Greater Than: Dotted Line <-----> Less Than or Equal /Greater Than or Equal: Solid Line Step 3: Shade above or below the line

Step 3 Shading: Shade where the points are TRUE!!!! > Above < Below

Example: Step 1: Graph the line (y = mx + b) Step 2: Boundary Lines DOTTED or SOLID Line? Step 3: Shade ABOVE or BELOW?

Definitions A system of linear inequalities is two or more inequalities in the same variables. Remember to shade when you graph! The solution to a system of linear inequalities is the shaded region that satisfies both linear inequalities.

**Graph one line at a time following our 3 steps.** Solve the system of linear inequalities by graphing. The graph shows ALL possible solutions to the system.

Solve

You try! Solve

You try! Solve