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**Linear Inequalities in 2 Variables**

3.3 Linear Inequalities in 2 Variables

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**OBJECTIVES: Solve and Graph a linear inequality in 2 variables.**

Use a linear inequality in 2 variables to solve real-world problems.

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**Definition: Linear Inequality in 2 Variables**

Using variables x & y, it is any inequality that can be written in one of the forms below, where A ≠ 0 and B ≠ 0. Ax + By ≥ C Ax + By > C Ax + By ≤ C Ax + By < C

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**SOLUTION… Ordered Pair (x, y)**

A region of the coordinate plane & is called a half-plane bounded by a boundary line.

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**Graph: y < x + 2 Graph the line.**

Use a dashed line because the values on this line are not included in the solution Choose a point such as (0, 0) to test. Since (0, 0) satisfies the inequality, shade the region that contains the point

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**Graph: y ≥ -2x + 3 Graph the boundary line.**

Use a solid line because the values on this line are included in the solution Choose a point like (0, 0) to test Since (0, 0) does not satisfy the inequality, shade the region that does not contain this point.

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**Extra Examples, If Needed…**

y > -2x – 2 y ≤ 2x + 5

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GRAPH: x – 3y ≤ 3 Sometimes, you may need to solve for for y before graphing.

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Graph: 3x – 4y ≥ 4

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**SOLUTION to 1 variable equations**

A half-plane Graph: x > -2

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Example Graph: y ≤ -1

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ACTIVITY PG. 175

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Graph linear inequalities with one variable EXAMPLE 2 Graph ( a ) y < –3 and ( b ) x < 2 in a coordinate plane. Test the point (0,0). Because (0,0) is.

Graph linear inequalities with one variable EXAMPLE 2 Graph ( a ) y < –3 and ( b ) x < 2 in a coordinate plane. Test the point (0,0). Because (0,0) is.

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