Graphing Systems of Equations



Coordinate Algebra: Unit 2

Name___________________  Date_________________ Period________

Lesson 10: Solving Systems of Inequalities Guided Notes

|Standard and Skills |

|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 |

Part I: Graphing Inequalities

Graphing Linear Inequalities

Step 1: Graph the ___________________, which is the equation of the line.

Step 2: By looking at our ________________________, determine how to draw the line.

> or < will give us a _____________________ line.

[pic] or [pic] will give us a _________________ line.

Step 3: Determine which side of the boundary to __________________ in order to represent our__________________________________.

How do we know which side of the boundary to shade?

Step 1: We must pick an ordered pair to _____________________.

Step 2: We must _______________________ the ordered pair into our inequality to determine if it makes a _________________ statement or a ___________________ statement.

Step 3: If our statement is true we will shade _____________________ the point. If our statement is false we will shade ____________________ the point.

Example 1: Graph the inequality.

y > -3x + 2.

Name two possible solutions for the system.

Guided Practice

Graph and shade the following inequalities. Name 2 possible solutions for each system.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

(Put in y = mx+b form)

Part II: Solving Systems of Inequalities

We have learned that the solution of a linear system of equations occurs where the two lines _______________________________. Likewise, the solution of system of linear inequalities occurs where the two regions _________________________. Any ordered pair that lies in the _______________________________ is a solution.

Steps to Solving Systems of Inequalities

Step 1: Put all inequalities in ______________________ form.

Step 2: Graph the _______________________.

Step 3: Shade the ____________________ 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.

[pic]

Example 2: Solve the system of inequalities.

[pic]

Independent Practice

Solve each linear system of inequalities by graphing. Make sure to show your region of solution and identify at least two solutions to the system.

1. Solve [pic]

2. Solve [pic]

3. Solve [pic]

4. Solve [pic]

5. Solve [pic]

[pic]

6. Solve y > [pic]

y < [pic]

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