1. 2.7 Two-variable inequalities (linear) 3.3 Systems of Inequalities
Algebra 2
2.7 Two-variable inequalities (linear)
3.3 Systems of Inequalities

2. 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

3. Check your Skills
Choose any method to solve

4. 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.

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

6. 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

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

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

9. 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.

10. **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.

11. Solve

12. You try! Solve

13. You try! Solve