Algebra 1 Notes Lesson 7-5 Graphing Systems of Inequalities

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Presentation transcript:

Algebra 1 Notes Lesson 7-5 Graphing Systems of Inequalities

Mathematics Standards Patterns, Functions and Algebra: Generalize patterns using functions or relationships, and freely translate among tabular, graphical and symbolic representations. Patterns, Functions and Algebra: Describe problem situations by using tabular, graphical and symbolic representations. Patterns, Functions and Algebra: Solve systems of linear inequalities. Patterns, Functions and Algebra: Solve real-world problems that can by modeled using systems of linear equations and inequalities.

Vocabulary System of Inequalities - Two Inequalities together Solution – Shaded in section of a graph that satisfies BOTH inequalities

Steps Solve both inequalities for “y” Graph both inequalities Shade section satisfying both

Example 1 Solve the system of inequalities by graphing. y < 2x + 2

Example 2 Solve the system of inequalities by graphing. x – y < -1

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3 – x – x -y < -x – 1

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3 – x – x -y < -x – 1 -1 -1 y > x + 1

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3 x – y > 3 – x – x -y < -x – 1 -1 -1 y > x + 1

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3 x – y > 3 – x – x – x – x -y < -x – 1 -1 -1 y > x + 1

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3 x – y > 3 – x – x – x – x -y < -x – 1 -y > -x + 3 -1 -1 y > x + 1

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3 x – y > 3 – x – x – x – x -y < -x – 1 -y > -x + 3 -1 -1 -1 -1 y > x + 1

Example 2 Solve the system of inequalities by graphing. x – y < -1 x – y < -1 x – y > 3 x – y > 3 – x – x – x – x -y < -x – 1 -y > -x + 3 -1 -1 -1 -1 y > x + 1 y < x – 3

Example 2 y > x + 1 y < x – 3 No Solution

Homework Pg 397 12 - 28 (even) 39 - 43 (all)