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SOLUTION EXAMPLE 1 Graph a system of two linear inequalities Graph the system of inequalities. y > –x – 2 y 3x + 6 Inequality 1 Inequality 2 Graph both inequalities in the same coordinate plane. The graph of the system is the intersection of the two half-planes, which is shown as the darker shade of blue.

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EXAMPLE 1 Graph a system of two linear inequalities CHECK Choose a point in the dark blue region, such as (0, 1). To check this solution, substitute 0 for x and 1 for y into each inequality. 1 > 0 – 2 ? 1 > –2 1 6 1 0 + 6 ?

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EXAMPLE 2 Graph a system of three linear inequalities Graph the system of inequalities. y > –1 x > –2 Inequality 1 Inequality 2 x + 2y 4 Inequality 3 SOLUTION Graph all three inequalities in the same coordinate plane. The graph of the system is the triangular region shown.

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GUIDED PRACTICE for Examples 1 and 2 ANSWER Graph the system of linear inequalities. 1. y < x – 4 y –x + 3

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GUIDED PRACTICE ANSWER Graph the system of linear inequalities. 2. y –x + 2 y < 4 x < 3 for Examples 1 and 2

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GUIDED PRACTICE ANSWER Graph the system of linear inequalities. 3. y > –x y x – 4 y < 5 for Examples 1 and 2

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3.4 Solving Systems of Linear Inequalities ©2001 by R. Villar All Rights Reserved.

3.4 Solving Systems of Linear Inequalities ©2001 by R. Villar All Rights Reserved.

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