270 Chapter 3 Systems of Linear Equations and Inequalities Section 3.5 Linear Inequalities and Systems of Linear Ax By 6 C, Ax By 7 C, Ax By C, x y 6 6 Ax By C Graphing a Linear Inequality in Two Variables Step 1 Solve for y, if possible. Step 2 Graph the related equation. Draw a dashed line if the inequality is strict, or . Otherwise, draw a solid line. Step 3 Shade above or below the line as follows: • Shade above the line if the inequality is of the form y 7 mx b or y mx b. • Shade below the line if the inequality is of the form y 6 mx b or y mx b. Note: A dashed line indicates that the line is not included in the solution set. A solid line indicates that the line is included in the solution set. This process is demonstrated in Example 1. Graphing a Linear Inequality in Two Variables Graph the solution set. Solution: Solve for y. 3x y 1 y 3x 1 Next graph the line defined by the related equation y 3x 1. Because the inequality is of the form y mx b, the solution to the inequality is the region below the line y 3x 1. See Figure 3-9. Skill Practice Graph the solution set. 1. 2x y 4 3x y 1 Example 1 y 5 4 3 1 Figure 3-9 x 1 2 3 4 5 5432 2 1 2 3 4 5 1 Answer 1. y x 1 5 4 3 1 2 3 4 5 5432 2 1 2 3 4 5 1 Inequalities in Two Variables Concepts 1. Graphing Linear Inequalities in Two Variables 2. Compound Linear Inequalities in Two Variables 3. Graphing a Feasible Region 1. Graphing Linear Inequalities in Two Variables A linear inequality in two variables x and y is an inequality that can be written in one of the following forms: or , provided A and B are not both zero. A solution to a linear inequality in two variables is an ordered pair that makes the inequality true. For example, solutions to the inequality are ordered pairs (x, y) such that the sum of the x- and y-coordinates is less than 6. This inequality has an infinite number of solutions, and therefore it is convenient to express the solution set as a graph. To graph a linear inequality in two variables, we will follow these steps.
miller_intermediate_algebra_4e_ch1_3
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