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SECTION 4-3: SYSTEMS OF LINEAR INEQUALITIES Goal: Graph, write and use a system of linear inequalities

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Warm-Up Graph y < x + 2

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Definitions System of linear inequalities in two variables consists of two or more linear inequalities in the same variables. Solution of a system of linear inequalities is any ordered pair that is a solution of each inequality in the system.

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Example 1: Check whether (4, 2) is a solution of the system of inequalities. a. x + y > -2b. x – 3y < 4 x – y > 4 x > 1

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Checkpoint: Check whether (3, -1) is a solution of the system of inequalities. 1. x + y > 12. -2x + y 4 y 6 3x + 4y > 8

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Definition: Graph of a system of linear inequalities shows all solutions of the system.

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Graph the system. y -x - 1

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Graph the system.y -1

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Graph the system. x > -3 x + 2y < 4

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Graph the system. x + y > 4 2x – y > 3

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Graph the system. x > 2 y > -2 3x + 2y < 12

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Graph the system in 3 variables. x > 0 y > 0 x + y < 5

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Graph the system in 3 variables. x > 0 y > 2 y < 2x + 6

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Graph the system in 3 variables. x 5

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HOMEWORK: P. 188-189 11-15 ODD, 23-28, 31-37 ODD, 43

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